A01:
ACTIVE CONTROL OF SOUND
AND VIBRATION

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0119

Convergence property of adaptive algorithms for engine soundcontrol
Wakana HISAGI1; Shunsuke ISHIMITSU1
1

Graduate School of Information Sciences, Hiroshima City University, Japan

ABSTRACTEngine sound is one of the most critical factors affecting the product value of motorcycles.
Although the spread of electric motorcycles whose engine sound is quiet is increasing, it expects totake longer until it is shifted entirely from the view of enough installation of charge equipment or its
high price. In other words, we can say that there is still a demand engine motorcycle. Personal
preferences for engine sound are also different for each person. Therefore, there is a need to develop
an active noise control (ANC) system that can change the sound quality and enable the design of an
ideal engine sound. The filtered-x least mean squares (FxLMS) algorithm has been widely used in
ANC systems. However, it is incapable of following fast-changing engine noise. By contrast, thesingle-frequency adaptive notch (SAN) algorithm enables high-speed processing using scalar
operations. Therefore, we compared control performance between LMS and SAN algorithms and asimulation of accelerated engine noise control using the SAN algorithm. The results indicated that theFxSAN algorithm has an excellent tracking performance and can be controlled for multiple frequency
components.
Keywords: Active noise control, Active sound quality control, Engine sound, Filtered-x LMS algorithm,
Filtered-x SAN algorithm

1. INTRODUCTION
In the modern world, automobiles have become essential to our lives. However, with thewidespread use of automobiles, noise pollution due to engine noise has become an issue. Although
the engine is required to be quiet, the perception of engine noise is also an essential element of an
automobile that gives a sense of acceleration and sportiness (1). Therefore, focusing solely on engine
quietness might lower the value of the product. Although every company is particular about the soundquality of its products, the definition of " the ideal engine sound" differs from person to person (2).
Therefore, it is necessary to realize a sound quality control system that adapts the sound to individual
preferences without compromising product value while also ensuring environmental friendliness.
The design of engine sound can be achieved by increasing or decreasing an arbitrary frequency
range. For this purpose, a system that can follow and control rapidly changing engine noise is required.
The filtered-x least mean squares (FxLMS) algorithm has been used in conventional active noise
control (ANC), but its computational complexity makes it difficult to follow fast -changing engine
speed (3). In a previous study (4), the single-frequency adaptive notch (SAN) algorithm was used tocontrol the narrow-band noise generated during the run of a four-wheeled vehicle. The results
confirmed that the algorithm was effective in reducing the targeted degree components and had a hi ghtracking performance.
In this study, we considered the possibility of sound design for engine noise by increasing or
decreasing an arbitrary frequency using the SAN algorithm. First, we compared the control
performance of the FxSAN algorithm with that of the FxLMS algorithm to confirm the effective noise
1hisagi@sd.info.hiroshima-cu.ac.jp

reduction effect of the FxSAN algorithm. Then, to control the engine noise, which changes infrequency with a change in speed, we investigated a control method that can follow the engine noise
faster.

2. METHODS
2.1 Filtered-x LMS algorithm
A block diagram of the filtered-x LMS algorithm is shown in Figure 1. The control signal 𝑦(𝑛) is
the output obtained by the convolution of the reference signal 𝑥(𝑛) and adaptive filter ℎ(𝑛); theoutput 𝑧(𝑛) is obtained by the convolution of 𝑦(𝑛), and 𝑐 is the error path characteristics up to thecontrol point. In the LMS, ℎ(𝑛) is updated according to the steepest descent method to minimize theerror 𝑒(𝑛) between 𝑧(𝑛) and the desired signal 𝑑(𝑛) . 𝑐̂ is the modeling error path measured
previously when the ANC system is configured (5).

Figure 1 – Block diagram of the filtered-x LMS algorithm (5)2.2 Filtered-x SAN algorithm
SAN is an algorithm that uses an adaptive notch filter for a single frequency (6). The reference
signal in the adaptive notch filter is a sinusoidal wave, and two filters are used for each target
frequency. Usually, 𝑥𝑐 (n) is generated by passing 𝑥𝑠 (𝑛) through a 90°phase shifter. Its multiplexing
capability enables the control of multiple frequencies.

Figure 2 – Block diagram of the filtered-x SAN algorithm (6)3. Comparison of control performance using a steady running sound
Noise control simulations using the FxLMS algorithm and FxSAN algorithm were conductedusing the sound of a motorcycle engine. The sound data were obtained at 3000 rpm during steady
and acceleration runs. Figure 3 shows the frequency characteristics of the steady running engine
sound operated from 0 Hz to 300 Hz. In this experiment, three frequency components ( 50 Hz, 100
Hz, and 150 Hz) were simulated as control targets.
Figures 3 and 4 show the frequency characteristics after control by the FxLMS and FxSAN
algorithms, respectively; Figure 5 shows the mean square error with respect to time.

Figure 3 – Frequency characteristics of a 3000-rpm steady running engine sound controlled by
FxLMS algorithm

Figure 4 – Frequency characteristics of a 3000-rpm steady running engine sound controlled byFxSAN algorithm

Figure 5 – Mean square error of frequency characteristics of a 3000-rpm steady runningengine sound controlled by FxLMS and FxSAN
Although both FxLMS and FxSAN were able to reduce the three target frequency components,
reduction by FxSAN was approximately 5-10 dB greater than that by FxLMS. The convergence speedof the mean square error was also faster in FxSAN than in FxLMS by approximately 0.1 s. From theseobservations, we can infer that the convergence performance for a specific frequency is better with
SAN as compared to LMS; and that the SAN algorithm is more suitable for noise control. If theadaptive filters used in the algorithm are vectors, all the filter elements must be accumulated andsummed, resulting in a large number of operations; the SAN algorithm with a scalar filter uses a muchsmaller number of operations resulting in a faster convergence than that of the former.

4. SAN control for accelerated running soundThe actual running engine sound is constantly changing because of acceleration and deceleration.
To use the changing engine noise as a reference signal for SAN control, a method to generate a sine
wave from the engine pulse was investigated. In the case of a four-cylinder engine, each cylinder
performs intake, compression, combustion, and exhaust during two revolutions of the crankshaft. In
other words, two explosions occur for each revolution of the crankshaft. Therefore, the pulse input ishalf of the crankshaft revolution. Therefore, the pulse input is half that of the crankshaft revol ution.
Based on this relation, the following procedure was used to generate a sine wave from the engine
pulse:
1.
2.
3.

The threshold value was set, and the noise was removed from the pulse data.
The time instances at which the pulses rise were recorded.
The time for two pulses was calculated and converted to frequency.

Because this method uses the time between the pulses as the period, it cannot follow the frequencychange in less than one period.
We implemented the SAN control with a sine wave generated from the pulses as the reference
signal; the acceleration engine sound was used as the desired signal. Figures 6 and 7 show the
spectrograms before and after the control, respectively. An overall reduction of approximately 20 dB
was obtained after the control, indicating that the generated reference signal was able to follow theacceleration engine sound.

Figure 6 – Spectrogram before the control

Figure 7 – Spectrogram after the control
However, the SAN algorithm used in this experiment was a single system, and the reference signal
was a single frequency signal based on the amplitude characteristics shown in Figure 8. Therefore, it
is unlikely that the generated reference signal will reduce the multiple components included in thedesired signal.

Figure 8 – Amplitude characteristics of the reference signal
To investigate this phenomenon further, we conducted a SAN control simulation using a
combination of simple and uncorrelated frequency signals. The desired signal was a 5 Hz sine wave,
and the reference signal was a 2 Hz sine wave; the magnitude of the 5 Hz component was reduced, as
shown in Figure 9.

Figure 9 – Amplitude characteristics of SAN control with uncorrelated frequency combinations
These results show that the 5Hz component is included in the control signal at the step ofcalculating the error signal. Therefore, we analyzed the signals generated at each step of the control.
Figure 10 shows the time variation of the outputs from two adaptive filters.

Figure 10 – Time-variation of outputs from adaptive filters

Figure 11 – Control signals before addition

Figure 12 – Control signals after addition
The adaptive filter output is a time-varying system that oscillates with time as it is updated. As thecontrol signal is calculated by the product of the reference signal and the filter coefficients, the desired
signal also contains multiple control target components. Subsequently, the control signal has areduction effect on the peak components of the desired signal. Figures 11 and 12 show the control
signals before and after adding sine and cosine waves, respectively.
Each signal contains multiple frequencies before addition; however, they cancel each other out
after the addition, and a signal only containing 5Hz, a component of the desired signal, is generated.
We infer from the results as mentioned earlier that in the control of signals with periodic components
by the SAN filter, the filter coefficients are affected by the error signal; and that th e control signal
contains components of the desired signal, thus realizing the control of multiple peak components.

5. CONCLUSIONSIn this study, we developed an algorithm for optimal control sound of a motorcycle engine byconducting noise control simulations of the FxLMS algorithm, which has been used in the past, andthe FxSAN algorithm, which is effective for signals with periodic components and requires lesser
computations compared to the former. In order to compare the control performance, control
simulations were conducted for specific frequency components in the steady running engine noise. In
addition, we investigated a control method that follows the noise of an accelerated driving engine andattempted to speed up the adaptation algorithm.
The comparison of control steady running engine sound led to the following observations.
Although both algorithms showed a reduction effect, the control efficiency of the SAN filter was
superior to that of the LMS filter in terms of the amount of reduction and conve rgence speed.
For the SAN control of accelerated engine noise, a method of generating a sine wave from engine
pulses was devised, and control simulations were conducted using the generated sine wave. It was
confirmed that the excellent tracking performance of the FxSAN algorithm and its control for multiple
frequency components through the time-varying oscillation of the adaptive filters' outputs.
In the future, we plan to study the tracking method for engine noise that changes in frequency
within one cycle and to conduct simulations using actual data to clarify the acceleration tracking
performance.

REFERENCES
1. Shibatani N, Ishimitsu S, Yamamoto M. Command filtered-x LMS algorithm and its application to car

interior noise for sound quality control. International Journal of Innovative Computing, Information andControl. 2018;14(2):647-656.
2. Murai K, Ishimitsu S. Sound Quality Control with Individual Preference Adaptation for Engine
Sound. International Journal of Biomedical Soft Computing and Human Sciences: the official journal of
the Biomedical Fuzzy Systems Association. 2020;25(1):23-27.
3. Hinamoto Y, Sakai H. Analysis of the filtered-X LMS algorithm and a related new algorithm for active
control of multitonal noise. IEEE transactions on audio, speech, and language
processing. 2005;14(1):123-130.
4. T. Inoue. Active noise control technology in automobiles. Journal of the Society of Instrument and Control
Engineers. 2012;51(12):1143-1149.
5. Stinson M, Daigle G. Meteorological measurements for use in sound propagation calculations. Proc 7thLong Range Sound Propagation; 24-26 July 1996; Ecully, France 1996. p. 137-47 Nishimura M, Usagawa
T, Ise S. Active noise control. Corona publishing Co., Ltd.: 2006.
6. Widrow B, Stearns SD. Adaptive Signal Processing. Englewood Cliffs, New Jersey, USA: Prentice-Hall;
1985.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0130

Active Noise Control for Coffee Maker
Julia REGALA1; Cheng-Yuan CHANG2
1

Chung Yuan Christian University, Taoyuan City, Taiwan

2

Chung Yuan Christian University, Taoyuan City, Taiwan

ABSTRACT
Commercially available coffee maker machines produce noise with low-frequency components. To reducethese noises, the filtered-x least mean square (FXLMS) algorithm with a feedback active noise control (ANC)
structure is used to reduce the narrowband noise. The noise is simulated by a recording of a coffee makermachine, played in a Styrofoam box, to mimic the environment. To assess system performance, microphones
are placed around the box to monitor the noise sound level at each location.
Keywords: Feedback Active Noise Control, Digital Signal Processing, Coffee Machine

1. INTRODUCTION
According to Jackson and Leventhall (1), the kitchen area is most often the noisiest room in thehouse because of the different appliances. These noises, which range from 40 to 90 dbA, are typicallygenerated during the daytime than the nighttime and are considered one of the most irritating noisesthat cause disruption to a time of relaxation. One of the most common home appliances used in the
kitchen during the daytime is the coffee machine. The reason for this is that drinking coffee in themorning provides a lot of positive effects. These include a boost in the energy in our bodies and ourability to concentrate on our tasks for the day (2).
Nowadays, a lot of consumers in the coffee drinking market buy the capsule/pod coffee machine
type. It is easy to use, portable and can offer consumers a variety of flavors by the cup. This increasein sales may also be due to the COVID-19 pandemic that pushed people to work from home (3, 4).
The capsule coffee machine uses a pump for the continuous flow of water depending on the type ofcoffee drink (5). Even though this machine produces noise in a short time, typically from 20 seconds
to 1 minute, this can still inflict irritation to the person brewing the coffee and to other people sleeping
in the house near the kitchen.
In this paper, Section 2 will discuss the proposed system which includes the noise analysis, control
system, and experimental setup. Section 3 will provide an analysis of the results obtained during theexperiment.

2. Proposed System
2.1 Coffee Machine Noise Analysis
To analyze the noise from the machine, a digital recorder was used to record the noise with asampling rate of 48kHz. The coffee machine that was used to acquire real coffee noise is the Nespresso
Mini Essenza De’Longhi. To avoid interference from any other noise source, the recording was
conducted inside an anechoic chamber located at the Active Noise and Vibration Control Laboratoryof Chung Yuan Christian University. The microphone was placed on the middle right side of themachine where the pump is located. In this position, a noise level reading of 80.3 dbA was obtainedusing a sound level meter. Based on Figure 1, this confirms that the noise is indeed narrowband whichmainly contains high energies from 60 Hz to 420 Hz. After that, the magnitude spectra continue todrop.

Figure 1 – Magnitude Spectra of the Coffee Machine Noise Recording
2.2 Feedback Active Noise Control
Feedback ANC systems are useful when the predictability of the signal is high (6). As seen in
Figure 2, the main idea of the feedback ANC system is to estimate the primary noise d(n) to serve as
the reference signal x(n) of the system given as
𝑀−1𝑥(𝑛) = 𝑑̂ (𝑛) = 𝑒(𝑛) + ∑ 𝑠̂𝑚 𝑦(𝑛 − 𝑚)

(1)

𝑚=0

where M is the order of the FIR filter 𝑆̂(𝑧) and its coefficients represented as 𝑠̂𝑚 (𝑛), 𝑚 = 0, 1, . . . , 𝑀 −1. The reference signal is then filtered by the estimated secondary-path transfer function 𝑆̂(𝑧) ,obtained through the secondary offline modeling method, to produce the filtered reference signal
𝑥′(𝑛) given as
𝑀−1′(𝑥 𝑛) = ∑ 𝑠̂𝑚 (𝑛)𝑥(𝑛 − 𝑚)

(2)

𝑚=0

Together with the residual error signal e(n) and step size µ, these three parameters will update thefilter coefficients of W(z) through the filtered-X least mean square algorithm expressed as:
w1 (n + 1) = w1 (n) + x(n − 1)e(n)(3)
The adaptive filter will produce the secondary signal y(n) represented as
L −1y (n) =  w1 (n) x(n − l )

(4)

l =0

where L is the order of the FIR filter 𝑊(𝑧) and its coefficients represented as 𝑤1 (𝑛), 𝑙 = 0, 1, . . . , 𝐿 −1 (7).

d ( n)W ( z)Sˆ ( z )

x(n)

FXLMS

x(n) = dˆ (n)y ( n)S ( z)

y(n) - +∑e( n )Sˆ ( z )yˆ (n)+∑+Figure 2 – Block Diagram of Feedback Active Noise Control using FXLMS Algorithm
2.3 Experimental Setup
The experimental setup of this application is shown in Figure 3. The dimension of the box, which
has a height of 16.5 cm, a length of 20 cm, and a width of 13 cm was used to simulate the size of themain body of the Nespresso Mini Essenza De’Longhi coffee machine. Figure 4 (a) shows a single
loudspeaker (Tang Band, T1-1942SB) that is placed inside the center of the box to play the recorded
coffee machine noise resampled at 2kHz. This speaker was chosen due to its small dimensions and its
technical parameters. To cancel the noise, two secondary speakers (Tang Band, T1-1931S) are attachedto the center of the left and right sides of the inside of the box facing outwards as shown in Figure 4(b). This setup simulates the scenario of placing the anti-noise speakers inside the device to make theoverall system controlled therefore leading to the usage of the internal space to reduce the noise before
the noise propagates outside of the simulated casing. On each side of the box, namely the front, back,left, and the right side is one MEMS error microphone that is placed at the chosen distance of 5 cm
away facing the center of their respective side for a total of four MEMS microphones. Thesemicrophones are connected in series to get both the reference and residual signal. Additionally, aroundthe box are five microphones to monitor the global reduction. Monitoring microphones 1 to 4 areplaced approximately 25 cm away from the nearest corner of the box. Meanwhile, monitoring
microphone 0 was placed randomly on the edge of a shelf nearby.

Figure 3 – Experimental Setup

.(a)

(b)

Figure 4 – Loudspeaker configurations for (a) primary noise and (b) anti-noise

3. EXPERIMENT RESULTS AND ANALYSISThe implementation of this simulation uses the Texas Instruments DSK6713 DSP board with asampling rate of 2kHz. Subsections below will cover the magnitude response, impulse response, andnoise reduction around the simulated coffee machine that were obtained during the experiment.
3.1 Impulse and Magnitude Response of the Estimated Secondary Path
The estimated secondary path, which is the transfer function from the anti-noise to the residual
noise, was obtained using the secondary offline modeling method. Figure 5 shows both the impulse
response and the magnitude response of the estimated secondary path. The impulse response in Figure
5 (a) shows the convergence of the offline modeling by using a filter length of 100 and a step size of
0.09. The magnitude response gives us an idea of which frequencies will the loudspeakers havedifficulty producing due to their insufficient power. Based on Figure 5 (b), the performance of
frequencies below 200 Hz shows magnitude levels of less than 0 dB thus explaining the ineffectivenessof reducing noise at those frequencies.

(a)

(b)
Figure 5 – (a) Impulse response and (b) magnitude response of Ŝ(z)3.2 Noise Reduction on the error microphones
Figure 6 shows the ANC performance of the system with the blue line depicting the coffee machinenoise acquired while the ANC system is off and the red line depicting the acquired residual noise
when the ANC system is on. The ANC performance plots have an upper bound of 800 Hz since Figure
1 shows that the intensity of narrowband noises continues to drop after 800 Hz. The noise frequencies
lower than 300 Hz are lower in intensity in Figure 6 as compared to Figure 1 due to the frequency
response of the primary loudspeaker (8) which can only provide full power after 200 Hz. This willlead to a different peak from 120 Hz to 280 Hz. Using a filter length of 300 and a step size of 0.001,
the ANC system was able to effectively reduce frequencies from 200 to 800 Hz. Frequencies lower
than 200 Hz were not reduced due to the frequency response of the secondary loudspeakers as
mentioned above.

Figure 6 – ANC Performance at the Error Microphones
Table 1 – Sound Level Meter Reading in dbA at the Error Microphones
Left Error Mic

Front Error Mic

Right Error Mic

Back Error Mic

ANC Off

72.1

73.5

72.3

68.8

ANC On

68.1

68.7

70.3

65.3

Reduction

4

4.8

2

3.5

Table 1 shows the noise level reading at every error microphone position. When ANC is OFF, theaverage sound level reading of all error microphones was found to be at 71.2 dbA. Overall, an averageof 3.6 dbA noise reduction was attained around the error microphones with the least reduction at theright error microphone. It can be observed that the noise reduction is not the same for each position.
This is maybe due to the uneven orientation or placement of the loudspeakers.
3.3 Noise Reduction on the Monitoring Microphones
Figure 7 shows all the power spectral densities for each of the five monitoring microphones. WithANC Off, which is represented by a blue line, each microphone picks up different intensities of a
specific noise frequency. Most noise frequencies were diminished due to their distance from the main
source of the noise. A 300 Hz noise reduction can be seen on monitoring microphones M2 and M3
located at the back side when ANC is on.

(a)

(b)

(c)

(d)

(e)
Figure 7 – ANC performance at monitoring microphones (a) M0, (b) M1, (c) M2, (d) M3, and (e) M4

Table 2 – Sound Level Meter Reading in dbA at the Monitoring Microphones
M0

M1

M2

M3

M4

ANC Off

62.8

64

64.5

62.6

65.1

ANC On

51.3

56

54.2

55.3

54.1

Reduction

11.5

8

10.3

7.3

11

Table 2 shows the SPL reduction at each of the different monitoring microphones around the area.
The average noise reduction at the monitoring microphones was found to be approximately 10 dbA.
According to Lam et al. (9), this kind of noise reduction result is enough for global noise cancellation.
It can also be observed that M0, M2, and M4 had noise reductions of more than 10 dBA while M3 had
the least noise reduction of less than 10 dBA. This is due to the low noise reduction obtained aroundthe error microphones on the back and right sides of the box.

4. CONCLUSIONSThis paper presented a hardware simulation for the reduction of the coffee machine noise byimplementing a Feedback ANC system with the FXLMS algorithm. The experimental results showthat placing four error microphones at each side of the box for the reference signal and using two
secondary speakers for the anti-noise is enough to provide a noise reduction on frequencies 200 to
800 Hz on the error microphones thus leading to an average of 10 dBA global noise reduction on themonitoring microphones placed near the area.
In the real-time implementation of this in the future, it is important to understand the main sourcesof noise in the machine as well as the different control measures to be conducted to effectively achieve
global noise cancellation.

REFERENCES
1. Jackson G, Leventhall H. Household appliance noise. Applied Ergonomics. 1976;7(2):114.
2. Glade M. Caffeine—Not just a stimulant. Nutrition. 2010;26(10):932-938.
3. Samoggia A, Riedel B. Consumers’ Perceptions of Coffee Health Benefits and Motives for Coffee
Consumption and Purchasing. Nutrients. 2019;11(3):653.
4. Czarniecka-Skubina E, Pielak M, Sałek P, Korzeniowska-Ginter R, Owczarek T. Consumer Choices andHabits Related to Coffee Consumption by Poles. International Journal of Environmental Research andPublic Health. 2021;18(8):3948.
5. Barella S, Gruttadauria A, Mapelli C, Mombelli D. Anomalous corrosion phenomena observed onelectrovalves of coffee espresso machines. Engineering Failure Analysis. 2013;33:449-456.
6. Kuo S, Morgan D. Active noise control: a tutorial review. Proceedings of the IEEE. 1999;87(6):943-975.
7. Kuo, S.M.; Morgan, D.R. Active Noise Control Systems: Algorithms and DSP Implementations; Wiley:
New York, NY, USA, 1996.
8. T1-1942SB - 1" PP square full range module - TB SPEAKER CO., LTD. [Internet]. Tb-speaker.com.
Available from: http://www.tb-speaker.com/products/t1-1942sb
9. Lam B, Gan W, Shi D, Nishimura M, Elliott S. Ten questions concerning active noise control in the built
environment. Building and Environment. 2021;200:107928.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0133

Region Separation Control for Broadband Sounds
by Multiple Sources
Shoma KIKIUCHI1 , Akira MIKI1*, Shinya KIJIMOTO1 , Satoshi ISHIKAWA1 , Yosuke KOBA2 ,Toshio INOUE3 and Xun WANG3
1
2

Kyushu university, graduate school, Japan

Kyushu university, faculty of engineering, Japan3

Honda, R&D Co.,Ltd., Japan

ABSTRACTIn this paper, we propose a method to reproduce different broadband sounds in different regions in the same
sound space by appropriately controlling multiple sound sources. To achieve this, it is necessary to design a
suitable filter that enables broadband control in the time domain. The procedure of this method is shown
below. Firstly, obtain the transfer function from the sound sources to the control points at each target
frequency. Secondly, the frequency characteristics of the control filter of each sound source using acoustic
contrast control (ACC) based on the transfer function and find the impulse response of the control filter byperforming discrete inverse Fourier transformation. Finally, by passing the input signal of a sound source
through its corresponding control filter, the sound space can be divided into an acoustically bright zone anda dark zone.
Simulations and experiments are conducted, and the results show that the proposed method is effective todeliver different time series signals to different regions properly. Also, we consider the cause of reverberantlike noise that occurs during control.
Keywords: Acoustic Contrast Control (ACC), Region separation, Personal Audio Technology

1. INTRODUCTION
Sound that is comfortable for one person can be annoying noise for another. For example, in the passenger
compartment of a vehicle, if one wants to hear a radio in the driver's seat and the other wants to hear themusic in the back seat, it becomes noise except for the sound that each wants to hear. In such situation, it isdifficult to separate the sound field using physical barriers such as sound insulation walls, so several
researches are being conducted on methods to deliver sound only to those who want to deliver by using
directional speakers and personal audio technology. The method using a directional speaker [1] is outputting
two ultrasonic waves having different frequencies by using the directivity of the ultrasonic waves andreproducing the difference component audible sound. It is pointed out that this method has disadvantage suchthat the reproduction range of sound depends on the directivity of ultrasonic waves and the reproducibilityof bass is low.
Personal audio technology makes the audible region (Bright zone) and the inaudible region (Dark zone) by

adjusting gain and phase of each sound source outputs considering the time delay due to the distance ofmultiple sources. Acoustic Contrast Control (ACC) [2] is proposed as a method to maximize the acoustic
contrast. The acoustic contrast is defined as the ratio of acoustic energy between the Bright zone and the Dark
zone. However, this gives the optimum relative output relationship between each sound source at a single
frequency and is not intended for controlling broadband sounds. In this paper,
we propose a method to reproduce different broadband sounds in the different regions in the same space byappropriately controlling multiple sources using ACC.

2. METHOD OF DESIGNING CONTROL FILTER
2.1 ACC-γ method
ACC-γ method is a method of maximizing the ratio of acoustic energy between Bright zone and Dark zone,
and for controlling the sound field using multiple control sources as shown in Fig.1. 𝑞! is output of 𝑖-thcontrol source, 𝐺!,# is acoustic transmission characteristics from 𝑖-th control source to 𝑙-th control point.
The complex sound pressure 𝑃(𝑥) at certain position 𝑥 in Bright zone can be expressed by the following
equation,%𝑃(𝑥) = + 𝐺!,$ 𝑞! = 𝐆( .

(2.1)

!&'

Acoustic energy density of Bright zone 𝑒) is acoustic energy per unit volume.
𝑒) is expressed as follows,𝑒) =1
1 𝑃(𝑥)𝑃(𝑥)𝑑𝑉 .
𝑉) *!

(2.2)

Where 𝑉) is the volume of Bright zone. Substitute this in (2.1),1𝑒) = 𝐪+ 4 1 𝐆,+ 𝐆, 𝑑𝑉 5 𝐪 = 𝐪+ 𝐑 ) 𝐪 .
𝑉) *!

(2.3)

Where superscript character 𝐻 expresses Hermitian transposer. Also, acoustic energy density of Dark zone
𝑒- is derived in the same way. The ratio of 𝑒) to 𝑒- is expressed as follows,𝛾=𝑒) 𝐪+ 𝐑 ) 𝐪=.
𝑒- 𝐪+ 𝐑 - 𝐪(2.4)

Transform this relation, we can obtain following equation(𝑹.') 𝐑 ) )𝐪 = 𝛾𝐪 .

(2.5)

The eigenvector corresponding to the maximum eigenvalue of 𝐑.'- 𝐑 ) is the output of control sources which
the ratio γ of the acoustic energy between Bright zone and Dark zone.

Fig.1: Control sources and control area
2.2 Control filter of ACC
Fig.2 shows the procedure of designing control filter. 𝑁 is the number of discrete frequency points in thefrequency range in control area. 𝑀 is the number of control sources. Firstly, calculate the output of 𝑀
control sources by ACC-γ method at a certain frequency. The frequency characteristics of each control
sources are calculated by doing this for all the controlled frequencies at all 𝑁 points. Then, control filter
𝐹! (𝑖 = 1, ⋯ , 𝑀) is obtained by IFFT(Inverse Fast Fourier Transform) of this frequency characteristics ateach control sources.

Fig.2: Design flow of FIR filter

3. CONTROL SIMULATION IN THE TIME DOMAIN
3.1 Setting of control area and confirmation of control effectWe design characteristic filters as described previous section in the vehicle and analyze the control effect.
Fig.3 shows control settings. Bright zone is fixed the left side of the back seat and the size of Bright zone is
0.4m square. Dark zone is placed at driver's seat (the right side of the front seat) at 0.4 m front-to-back and0.4 m, 0.6 m, 0.8 m, and 1.0 m left-to-right. Fig.4 shows the result of analysis for the control effect per 1/3octave using white noise controlled under 7100Hz as input signal. In almost all frequency ranges, the control
effect tends to become worse as Dark zone becomes wider. This suggests that the wider Dark zone, the moredifficult it is to control the entire region. Also, the difference between average sound pressure level in Brightzone 𝐿/ (expressed in Equation (3.1)) and average sound pressure level in Dark zone 𝐿0 (expressed in Eq.
(3.2)) is more than 10 dB (this difference is χ (Eq. (3.3))). This indicates that the sound field is controlledfrom low to high frequencies. Where 𝑃1 is average sound pressure in Bright zone，𝑃2 is average soundpressure in Dark zone.
𝑃/
2 × 10.3
𝑃0
𝐿0 = 20log
2 × 10.3
𝐿/ = 20log

𝜒 = 𝐿/ − 𝐿0

Fig.3: Bright zone, Dark zone and sound sources placement

Fig.4: 1/3 octave control effect analysis for each size of Dark zone

(3.1)
(3.2)
(3.3)

3.2 Reproduction of sound in different regions of different time series signals
We verify whether the output of the control source which is the sum of news signal and music signal cangenerate a sound field with the Bright zone of news signal (BZ_news) on the left side of the back seat andthe Bright zone of music signal (BZ_music) on the driver's seat in the vehicle. The control field is 0.4m
square for both BZ_news and BZ_music. Fig.5 shows each input signal and sound pressure in Bright zone.
Table.1 shows correlation coefficient of sound pressure in Bright zone. Correlation coefficient with anabsolute value close to 1 indicates stronger correlation, and the positive or negative indicates the phase. The
absolute values of correlation coefficients are larger for the news signal in BZ_news and for the music signal
in BZ_music (Table.1). This indicates that the sound field is closer to the target sound field.

Fig.5: news signal (upper left) and sound pressure at BZ_news(lower left)
music signal (upper right), sound pressure at BZ_music(lower right)
Table.1: Correlation between input signals and sound pressure at Bright zone
News signal

Music signal

BZ_news

0.4658-0.0427

BZ_music

0.0218-0.6661

4. EXPERIMENTAL RESULTS IN THE ACTUAL VEHICLE
The control effect of analysis using acoustic characteristic in the vehicle is confirmed up to the previous
section. We confirm the control effect of proposed method in the actual sound field by outputting the control
output calculated by analysis from the control sources placed in the actual vehicle. The control sound isgenerated from each source for the source arrangement and the measurement range same as 3.2 clause, andwe verify the results. Table.2 shows correlation coefficients obtained in the experiment. Correlation
coefficient of news signal is larger than music signal in BZ_news and Correlation coefficient music signal islarger than news signal in BZ_music as a tendency of the control result. News signal is larger than musicsignal in BZ_news and music signal is larger than news signal in BZ_music same as simulation. Therefore,
different time series signals in the different regions can be generated at the same time under the actual
environment.

Table.2 : Correlation between input signals and sound pressure at Bright zone
News signal

Music signal

BZ_news-0.41410.2301

BZ_music-0.04420.6373

5. NOISE AFTER CONTROL
During the control with this proposed method, reverberant-like noise is observed. When the input signal isimpulse, comparison between frequency analysis of reverberation components in Bright zone and that ofcontrol filter is shown in Fig.6. According to Fig.6, the peak frequencies tend to coincide in both cases. In
order to this tendency, we suppose that control filter cause the noise.

Fig.6: Frequency analysis in Bright zone and control filter

6. CONCLUSIONSIn order to reproduce different signals in different regions of the same space, we developed a method tocontrol broad band signals in the time domain and verified the control effect. Through simulations andexperiments, we showed that the signal to be heard has correlation coefficient which is at least approximately
0.1 larger than the other signal in each control region, and that it is possible to separate the sound field. We
supposed that the reverberant-like noise generated during control is caused by the control filters.

REFERENCES
1.

Toshihiko Komatsuzaki, Kensuke Hatanaka, Yoshio Iwata,” Study on Active Noise Control using Highdirectiona1 Parametric Speaker”, Transactions of the Japan Society of Mechanical Engineers, Vol. 4,
No. 737 (2008-1).

2.

J.-W. Choi and Y.-H. Kim, “Generation of an acoustically bright zone with an illuminated region using
multiple sources” ，The Journal of the acoustical Society of America, Vol. 111, No. 4(2002), pp. 1695–
1700.

3.

Shutaro Shigetomi, “Sound field control by multiple sources to realize a comfortable soundenvironment”, Department of Mechanical and Aviation Engineering bachelor thesis, Kyushu University(2019).

4.

Akira Miki, Shinya Kijimoto, Satoshi Ishikawa, Yosuke Koba, Toshio Inoue, and Xun Wang” Acoustic
field control for region separation” Symposium on Environmental Engineering, vol.30 (2020).

5.

Akira Miki, Shinya Kijimoto, Satoshi Ishikawa, Yosuke Koba, Toshio Inoue, and Xun Wang” Acoustic
field control for region separation” Symposium on Environmental Engineering, vol.46 (2021).

6.

Akira Miki, “Region separation control for broadband sounds by multiple sources”, Department of
Mechanical Engineering master thesis, Kyushu University (2022)

ABS-0211

Study on feedforward active noise control system with optical laser
microphone utilizing proportional-integral-differential ﬁlter
Koki Nakamura(1) , Kenta Iwai(2) , Takanobu Nishiura(3) .
(1) Graduate School of Information Science and Engineering, Ritsumeikan University, Japan, is0421si@ed.ritsumei.ac.jp(2) College of Information Science and Engineering, Ritsumeikan University, Japan, iwai18sp@fc.ritsumei.ac.jp(3) College of Information Science and Engineering, Ritsumeikan University, Japan, nishiura@is.ritsumei.ac.jp

ABSTRACTIn this paper, a feedforward active noise control (ANC) system with an optical laser microphone utilizing a
proportional-integral-differential (PID) ﬁlter is proposed. The problem of a feedforward ANC system is a deterioration of noise reduction performance when it does not satisfy the causality constraint. The feedforward
ANC system with an optical laser microphone has been proposed to solve this problem. The conventional ANC
system utilized the optical laser microphone as the reference microphone to relax the causality constraint in
the feedforward ANC system and adopted the ﬁrst-order differentiator to the reference signal to increase thecoherence between the unwanted noise picked up by the reference and error microphones. However, the coherence between them becomes small at low frequencies by the differentiator and the noise reduction performance
deteriorates. To solve this problem, the feedforward ANC system with the optical laser microphone utilizing a
PID ﬁlter is proposed. By using the PID ﬁlter, the proposed ANC system can increase the coherence between
them at low frequencies while maintaining the advantage of the conventional ANC system. Simulation results
show that the proposed ANC system can reduce the unwanted noise well compared to the conventional ANC
system.

Keywords: Active noise control system, Optical laser microphone, PID

1

INTRODUCTION

Recently, the active noise control (ANC) systems have been developed, and the feedforward ANC system has
been actively studied among them [1]-[3]. The feedforward ANC system consists of a reference microphone,error microphone, and secondary loudspeaker. In the feedforward ANC system, the placement of the reference
and error microphones is important to satisfy the causality constraint [5]-[8]. In other words, the anti-noise,
which is generated by using the reference signal, should reaches at the error microphone before the unwanted
noise reaches at the error microphone. If the feedforward ANC system does not satisfy the constraint, the noise
reduction performance of the feedforward ANC system must be reduced.
To relax the constraint, the feedforward ANC system with an optical laser microphone has been proposed[8]. Since this system utilizes the optical laser microphone [9], which can pick up the unwanted noise with avelocity of light of 3.0 × 108 m/s as the reference microphone, the causality constraint is relaxed compared withthe basic feedforward ANC system. In addition, the conventional ANC system adopted a ﬁrst-order differentiator
for the reference signal to increase the coherence between the reference signal and the unwanted noise picked
up by the error microphone. This is because the reference signal is picked up as the vibrating velocity andthe frequency spectrum of the reference microphone is different from that of the unwanted noise picked up by
the error microphone. However, the gain of the ﬁrst-order differentiator attenuates the reference signal at low
frequencies. Hence, the noise reduction performance of the conventional ANC system degrades.
To solve this problem, the feedforward ANC system with the optical laser microphone utilizing proportionalintegral-differential (PID) ﬁlter is proposed in this paper. Instead of the ﬁrst-order differentiator, the proposed

(a) Structure of basic feedforward ANC system(b) Block diagram of basic feedforward ANC system

Figure 1. Structure and block diagram of basic feedforward ANC system

ANC system adopts the PID ﬁlter which consists of the proportional, integral, and differential components toincrease the coherence between the reference signal and the unwanted noise. To evaluate the effectiveness ofthe proposed ANC system, some computer simulations were conducted.

2

FEEDFORWARD ANC SYSTEM AND ITS CAUSALITY CONSTRAINT

2.1 Feedforward active noise control system
The feedforward ANC system consists of a reference microphone, error microphone, and secondary loudspeaker.
Figure 1 shows the structure and block diagram of a basic feedforward ANC system. In Fig. 1, P, R, S W ,and Ŝ represent the primary path, reference path, secondary path, noise control ﬁlter, and secondary path model,
respectively.
In Fig. 1, the unwanted noise v(n) is picked up by the reference microphone, and then the noise control
ﬁlter w(n) is updated using the reference signal x(n). The anti-noise y(n) is genetated after updating the noise
control ﬁlter w(n), and it is emitted from the secondary loudspeaker. After that, the unwanted noise passed
through the primary path d(n) is reduced by the anti-noise y′ (n) through the secondary path. Here, the error
signal e(n) detected at the error microphone is represented ase(n) =

d(n) − y′ (n),(1)

where n is the time index. In addtion, the anti-noise y′ (n) is represented asy′ (n) =y(n) =

sT (n)y(n),Tw (n)x(n),

(2)
(3)

where s(n) is the impluse response of the secondary path, T is the transpose operator, y(n) = [y(n), y(n −1), · · · , y(n − i), · · · ] is the anti-noise vector, w(n) = [w0 (n), w1 (n), · · · , wL−1 (n)] is the coefﬁcient of the noise
control ﬁlter, x(n) = [x(n), x(n − 1), · · · , x(n − L + 1)] is the reference signal vector, and L is the tap length of thenoise control ﬁlter w(n). The ﬁltered-x normalized least mean square (FxNLMS) algorithm [2], [4] updates the
cofﬁcient of the noise control ﬁlter. The coefﬁcient of the noise control ﬁlter w(n) is updated bye(n)x′ (n),∥x′ (n)∥2 + βw(n + 1) =w(n) + αx′ (n) =ŝT (n)x(n),

(4)
(5)

where x′ (n) = [x′ (n), x′ (n − 1), · · · , x′ (n − N + 1)] is the ﬁltered reference signal vector, N is the tap length of
the ﬁltered reference signal vector x′ (n), ∥x′ (n)∥2 is the norm of the ﬁltered reference signal vector x′ (n),α (0 < α < 2) is the step size parameter, β (0 < β << 1) is the regularization parameter, and ŝ(n) is the impluse
response of the secondary path model.
2.2 The causality constraint in the feedforward ANC system
In the feedforward ANC system, the sum of the acoustic delay from the unwanted noise to the reference
microphone, the computational time delay, and the acoustic delay from the secondary loudspeaker to the error

Figure 2. Principle of optical laser microphone

microphone should be smaller than the acoustic delay from the unwanted noise to the error microphone. The
relationship [8] is represented as
DP>

DR + DC + DS ,(6)

where DP and DR is the acoustic delay from the unwanted noise to the error and reference microphones,
respectively, DC is the computational time delay, and DS is the acoustic delay from the secondary loudspeakerto the error microphone. The relationship is called the causality constraint in the feedforward ANC system [5][8]. If the feedforward ANC system does not satisfy the causality constraint, the noise reduction performancedegrades. To relax the constraint, the feedforward ANC system with the optical laser microphone has been
proposed [8]. The next section describes the conventional ANC system.

3

CONVENTIONAL FEEDFORWARD ANC SYSTEM WITH OPTICAL LASER MICROPHONE

3.1 Optical laser microphone
The optical laser microphone emits an optical laser to the surface of a vibrating object and measures the soundas the vibration of the object with a velocity of light of 3.0 × 108 m/s. The principle of sound measurement by
the optical laser microphone is shown in Fig. 2. The beam emitted by the optical laser microphone is irradiatedto a vibrating object and becomes the reﬂected beam. Due to the Doppler effect, the reﬂected beam detectedby the optical laser microphone has a frequency difference compared with the emmited beam. By calculating
this frequency difference, the optical laser microphone measures the vibration velocity of the object.
3.2 Conventional feedforward ANC system with optical laser microphone
The structure and block diagram of the conventional ANC system with the optical laser microphone are shownin Fig. 3. The conventional ANC system utilizes the optical laser microphone as the reference microphone.
Therefore, the acousitc delay DR in (6) becomes small, and then the causality constraint is relaxed comparedwith the basic feedforward ANC system. However, the conventional ANC system utilizes an ordinary microphone (e.g., electret condenser microphone : ECM) as the error microphone. Hence, the characteristics of theunwanted noise which picked up by the reference and error microphones are different from each other. In otherwords, the unwanted noise which picked up by the reference microphone is for the velocity, whereas the unwanted noise which picked up by the error microphone is for the sound pressure. Hence, the coherence between
these signals becomes small, and then the noise reduction performance degrades [2], [8].
To solve this problem, the ﬁrst-order differentiator is adopted to the reference signal picked up by the
optical laser microphone. This is based on the relationship between the volume velocity of the air and thesound pressure [8], shown as
P(s) =krρsQ(s)es(t− ω ) ,
4π r

(7)

where P(s) and Q(s) are the Laplace transform of the sound pressure and volume velocity, s is the complex
variable, ω is the angular frequency, ρ is the air density, r is the distance between the sound source and themicrophone, and k is the wave number. From (7), the sound pressure P(s) can be expressed as the ﬁrst-orderdifferentiation of the volume velocity sQ(s). On the basis of this theory, the conventional ANC system estimates

(a) Structure of conv. feedforward ANC system(b) Block diagram of conv. feedforward ANC system

Figure 3. Structure and block diagram of conv. feedforward ANC system

the sound pressure at the reference microphone by the differentiation of the velocity picked up by the opticallaser microphone. The ﬁrst-order diifferentiator HD (z) is realized as
HD (z) =1 − z−1 ,(8)where z is the complex variable and HD (z) is the z-transfrom of the ﬁrst-order differentiator. The conventional
ANC system with the differentiator improves the noise reduction performance compared to the conventional
ANC system without it because of increase of the coherence between the unwanted noise picked up by thereference and error microphones.
3.3 Problem of the conventional feedforward ANC system
The conventional ANC system adopts the differentiator HD (z) in the ANC system to increase the coherence
between the unwanted noise picked up by the reference and error microphones. The frequensy response of thedifferentiator HD (z) with the sampling frequency of 8000 Hz is shown in Fig. 4, in which the white noise
is used as the unwanted noise. Here, the coherence between the unwanted noise picked up by the reference
and error microphones is shown in Fig. 5. In this paper, the magnitude-squared coherence (MSC) is used toevaluate the coherence. MSC is written as
MSC( f ) =|Pdx ( f )|2,
Pdd ( f )Pxx ( f )(9)where f is the frequency index, Pdx ( f ) is the cross power spectral density of the reference signal x(n) andthe unwanted noise d(n), and Pdd ( f ) and Pxx ( f ) are the power spectral densities of the unwanted noise d(n)and the reference signal x(n). From Fig. 5, the conventional ANC system with the differentiator has the greater
coherence than the conventional ANC system without the differentiator at above 100 Hz. On the other hand, theconventional ANC system with the differentiator has the smaller coherence than the conventional ANC system
without the differentiator at below 100 Hz. This is because the conventional ANC system with the differentiator
adopts a differentiator shown in Fig. 4 for the reference signal, and then the gain of the differentiator attenuates
the reference signal at low frequencies. Since the ANC system is effective to low frequency components ofnoise [2], its noise reduction performance degrades as the coherence at low frequencies is small shown in Fig.
5.

4

PROPOSED FEEDFORWARD ANC SYSTEM WITH OPTICAL LASER MICROPHONE

In this paper, the feedforward ANC system with the optical laser microphone utilizing a proportional-integraldifferential (PID) ﬁlter is proposed to solve the problem shown in sect. 3. The block diagram of the proposed
ANC system is shown in Fig. 6. The proposed ANC system utilizes the PID ﬁlter which consists of the
proportional, integral, and differential components in the feedforward ANC system. The PID ﬁlter HPID (z) is
written as
HPID (z) =KP + KI (1 + z−1 ) + KD (1 − z−1 ),(10)Figure 4. Frequency response of HD (z)Figure 5. Coherence of each ANC system

Figure 6. Block diagram of the prop. ANC system

Figure 7. Frequency response of HD (z) and HPID (z)where HPID (z) is the z-transform of the PID ﬁlter and KP , KI , and KD are the proportional, integral, anddifferential constants, respectively. From (10), the PID ﬁlter is characterized by the ratio of the proportional,
integral, and differential constants. That is, depending on the ratio of the these constants, the PID ﬁlter has
the characteristics of the differentiator while suppressing the attenuation at low frequencies. The frequency
response of the PID ﬁlter is shown in Fig. 7. In Fig. 7, the constants of KP , KI , and KD are 1, 100, 8000,
and the sampling frequency is 8000 Hz, respectively. From Fig. 7, the PID ﬁlter has the characteristics ofthe differentiator while suppressing its attenuation at low frequencies. Hence, the proposed ANC system canincrease the coherence beteween the reference signal and the unwanted noise picked up by the error microphone
at low frequencies and the other frequencies by large gain of the PID ﬁlter.

5

SIMULATION RESULTS

Simulation results are presented here to verify the effectiveness of the proposed ANC system. In the following
simulations, the effectiveness of the proposed ANC system is compared with that of the basic feedforward
ANC system, the conventional ANC system with the ﬁrst-order differentiator, and the conventional ANC system
without the ﬁrst-order differentiator. Hereafter, the conventional ANC system with the ﬁrst-order differentiatorand without the ﬁrst-order differentiator are called the conventional ANC system with the differentiator andthe conventional ANC system without the differentiator. In addition, the identiﬁed impulse responses of eachpath are measured in a soundproof room by the NLMS algorithm, and were used in the simulations. The
measurement setup and conditions are shown in Fig. 8 (a) and Table 1, respectively. The identiﬁcation system

(a) Measurement setup(b) Implementation of identiﬁcation system

Figure 8. Measurement setup and implementation for the identiﬁcation of each path(a) Primary path(b) Ref. path using ECM(c) Ref. path using optical laser mic.

(d) Secondary path

Figure 9. Impulse responses of each path(a) Primary path(b) Ref. path using ECM(c) Ref. path using optical laser mic.

(d) Secondary path

Figure 10. Frequency responses of each path

was implemented as shown in Fig. 8 (b). The identiﬁed impulse responses and their frequency responsies areshown Figs. 9 and 10.
Table 2. Simulation conditons
Table 1. Identiﬁcation conditions
Noise source
Sampling frequency
Frequency range
Update algorithm
Tap length of adaptive ﬁlter
Step size parameters
Regularization parameters

White noise
8000 Hz0−2000 Hz
NLMS
300
1.0 × 10−2
1.0 × 10−6

Unwanted noise 1
Unwanted noise 2
Sampling frequency
Frequency range
Tap length of each path P, R, S
Tap length of secondary path model Ŝ
Tap length of adaptive ﬁlter W
Update algorithm
Step size parameters
Regularization parameters

White noise
Pink noise
8000 Hz0−2000 Hz
300
300
300
FxNLMS
1.0 × 10−2
1.0 × 10−6

(a) Unwanted noise 1(b) Unwanted noise 2

Figure 11. Amount of noise reduction

5.1 Simulation results
The amount of noise reduction were evaluated at each ANC system. The amount of noise reduction is deﬁned
byReduction(n) = 10 log102∑N−1
m=0 d (n − m),N−1 2∑m=0 e (n − m)(11)where m is time index and N is the frame length. In these simulations, the amount of noise reduction was
calculated every 2400 samples. Simulation conditions are shown in Table 2. Due to the performance limitsof the ANC system, the frequency ranges of the unwanted noise 1 and 2 were limited to 0−2000 Hz. The
amount of noise reduction for each ANC system is shown in Fig. 11. Figure 11 (a) shows that both theproposed ANC system and conventional ANC system with the differentiator reduce the unwanted noise as sameamount as the basic ANC system. On the other hand, Fig. 11 (b) shows that the noise reduction performanceof the conventional ANC system with the differentiator is smaller than that of the other systems. This isbecause the unwanted noise 2 is pink noise which has large gain at the low frequencies. If the unwanted
noise has large power at low frequencies, the noise reduction performance of the conventional ANC systemwith the differentiator degrades due to the attenuation of the coherence at low frequencies by the gain of thedifferentiator. On the other hand, from Fig. 11 (b), the proposed ANC system reduces the unwanted noise
almost the same amount as the basic ANC system due to the large gain of the PID ﬁlter, which makes thecoherence between the unwanted noise picked up by the reference and error microphones. These results indicate
the proposed ANC system can reduce the unwanted noise compared with the conventional ANC system withdifferentiator.
Also, the causality constraint of the proposed ANC system was evaluated by the identiﬁed impulse responsesof each path. From Fig. 9, the delay of each path are DP = 7.5 ms, DS = 1.25 ms, DR = 4.5 ms for the electretcondenser microphone, and DR = 2.25 ms for the optical laser microphone, respectively. These results indicatethat the computational time delay DC for the proposed, conventional, and basic ANC systems should be DC < 4
ms, DC < 4 ms, and DC < 1.75 ms. Therefore, the proposed ANC system can relax the causality constraint in
the feedforward ANC system and avoid the degradation of the noise reduction performance due to the violationof the causality constraint.
Finally, the coherence between the unwanted noise picked up by the reference and error microphones wascalculated by the MSC shown in (7) to evaluate the effectiveness of the PID ﬁlter. In the calculation of thecoherence, x(n) is replaced by xD (n) and xPID (n) for the conventional ANC system with the differentiator andproposed ANC system. The MSC for each ANC system is shown in Fig. 12. From Fig. 12, the MSC of
the proposed ANC system is greater at low frequencies (0-100 Hz) and comparable to the conventional ANC
system with the differentiator at the other frequencies. These results show that the PID ﬁlter can increase thecoherence between these signals compared to the differentiator.

(a) Unwanted noise 1(b) Unwanted noise 2

Figure 12. Coherence of each ANC system

6

CONCLUSIONSIn this paper, a feedforward ANC system with the optical laser microphone utilizing the PID ﬁlter is proposed.
The conventional ANC system utilized the optical laser microphone as the reference microphone to relax thecausality constraint in the feedforward ANC system and adopted the ﬁrst-order differentiator in the ANC system to increase the coherence between the unwanted noise picked up by the reference and error microphones.
However, the gain of the ﬁrst-order differentiator attenuates the reference signal at low frequencies. Hence, thenoise reduction performance of the conventional ANC system degrades. To solve this problem, the proposed
ANC system utilizes the PID ﬁlter which consists of the proportional, integral, and differential components toincrease the coherence between the reference signal and the unwanted noise instead of the differentiator. By
using the PID ﬁlter, the proposed ANC system can increase the coherence between them at low frequencies
while maintaining the advantage of the conventional ANC system. Simulation results show that the proposed
ANC system can reduce the unwanted noise well compared to the conventional ANC system. In the future,
we will consider the optimization methods for each constant of the PID ﬁlter and conduct the noise reduction
experiment in a real environment.

ACKNOWLEDGEMENTS
This work was partly supported by the Ritsumeikan Global Innovation Research Organization (R-GIRO), andby the JSPS KAKENHI Grant Numbers JP19H04142, 21H04427, 21H03488 and 21K18372.

REFERENCES[1] S. M. Kuo and D. R. Morgan, “Active Noise Control Systems: Algorithms and DSP Implementations,” New
York: John Wiley and Sons, 1996.
[2] S. M. Kuo and D. R. Morgan, “Active Noise Control: A Turtorial Review,” Proc. IEEE, vol. 87, no. 6, pp.
943–973, 1999.
[3] Y. Kajikawa, W. S. Gan, and S. M. Kuo, “Recent advances on active noise control: open issues and innovative applications,” APSIPA Trans. Signal Inform. Process., vol. 1, pp. 1–21, 2012.
[4] E. Bjarnason, “Analysis of the ﬁltered-x LMS algorithm,” IEEE Trans. Speech Audio Process., vol. 3, no.
6, pp. 504–514, 1995.
[5] P. A. Nelson, J. K. Hammond, P. Joseph, and S. J. Elliott, “Active control of stationary random soundﬁelds,” J. Acoust. Soc. Amer., vol. 87, no. 3, pp. 963–975, 1990.
[6] R. A. Burdisso, J. S. Vipperman, and C. R. Fuller, “Causality analysis of feedforward-controled systems
with broadband inputs,” J. Acoust. Soc. Amer., vol. 94, no. 1, pp. 234–242, 1993.
[7] X. Kong and S. M. Kuo, “Study of causality constraint on feedforward active noise control systems,” IEEE
Trans. Circuits Syst., vol. 46, no. 2, pp. 183–186, 1999.
[8] K. Iwai and T. Nishiua, “Study on feedforward active noise control system with optical laser microphone
to detect reference signal with short delay,” APSIPA ASC 2020, pp. 266–271, 2020.
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PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0220

Preconditioning FxLMS algorithms and their applications to engine
noise control
Liping ZHU1,2; Xiaojun QIU1; Sheng WU1; Dongxing MAO2; Xu ZHONG1;
1
2

Shanghai Huawei Technology Co. Ltd, Shanghai, 200092, China

School of Physical Science and Engineering, Tongji University, Shanghai, 201206, China

ABSTRACT
LMS-based algorithms is widely used for active noise control systems. However, their noise reduction
performances and convergence rates are affected by the characteristics of references signals and secondary
paths. It is known that preconditioning LMS algorithms can alleviate the problem by compensating secondary
paths to have flat frequency responses and whitening reference signals. In the paper, two methods of
preconditioning FxLMS algorithms, minimum-phase/all-pass decomposition and singular value
decomposition, are analyzed and discussed. Their applicability and performances in terms of convergence
rate and noise reduction are compared for both single- and multi-channel systems. Simulations are performed
using singular value decomposition to control engine noise with the data and secondary paths recorded inside
a car.
Keywords: Active noise control, Preconditioning algorithms, Engine noise control

1. INTRODUCTION
The filtered reference least mean squares (FxLMS) algorithm is the most popular algorithm foractive noise control (ANC) systems(1). However, its convergence rate, which depends on thecharacteristics of reference signals and secondary paths, is slow(2). Thus, measures have to be taken
to accelerate the convergence rate(3).
It has been shown that the maximum step size to ensure the stability for an A NC system isdetermined by the magnitudes of the reference signals and frequency responses at the corresponding
frequency (4). For engine harmonic noise or broadband noise, since the secondary path responses atthese frequencies are different, a standoff step size has to be chosen, which leads to a slow
convergence rate for some frequency components(5).
To tackle the problem, some preconditioning algorithms have been proposed. A minimumphase/allpass decomposition had been proposed to process reference signals and secondary paths by
Elliott, which whitens, decorrelates reference signals and decouples secondary paths(6). With thesemeasures, the algorithm could achieve a fast convergence rate(7). However, for a general multichannel system, computing minimum-phase/allpass components are difficult. A singular value
decomposition (SVD) method was explored to replace the minimum-phase/allpass decomposition(8).
But extra delays are introduced by SVD. To compare their performances in detail, the processing
results of above two measures are analyzed in the paper and engine noise control using the FxLMS
algorithm with SVD is simulated.
The paper is organized as follows: theories are introduced in Section 2, decomposing results ofsecondary paths and reference signals are compared in Sections 3 and 4. The simulation results arepresented in Section 5. In Section 6, conclusions are derived.

2. THEORY ANALYSIS
In this section, two existing preconditioning algorithms are introduced and compared
theoretically(6,8). The diagrams of two algorithms are shown in Figures 1(a) and (b), respectively,
where P(z) and S(z) denote the primary path and secondary path. Different from the original references,1

zhuliping15@huawei.com

the decomposition methods of references signals and secondary paths are applied to the FxLMS
algorithm, rather than the FeLMS algorithm(a) Proposed in Ref. [6](b) Proposed in Ref. [8]Figure 1 – Diagrams of preconditioning FxLMS algorithms
2.1 Minimum-phase/Allpass Decomposition
Assuming the power spectral density of the reference signals x(k) is S xx (z)，the spectral factorization
F(z) in Figure 1(a) can be derived as
F ( z ) = FFT{u (n)IFFT[log e ( S xx )]}(1)
where u(n) is a causality constraint vector and is 0 for n<0, 0.5 for n=0 and 1 for n>0(7).
The reference signals are whitened tov( z ) = F −1 ( z ) x( z )(2)Similarly, the minimum-phase component of the secondary path can be obtained as(3)Sˆmin ( z) = FFT{u(n)IFFT[loge (| Sˆ ( z) |2 ]}where Sˆ ( z) is the identified result of the secondary path S (z).
The corresponding allpass component is−1
Sˆall ( z) = Sˆmin( z )Sˆ ( z )(4)ˆFigure 1(a) shows that the output of the control filter W(z) is compensated by the inverse of Smin ( z) ,which means only allpass component of the secondary path is left. Thus, for the FxLMS algorithm,
the reference signals only need to be filtered by the allpass component Sˆall ( z ) of the secondary path.
2.2 Singular Value Decomposition
The method decomposes power spectral density of the reference signals Sxx (z) into following form
S xx ( z ) =Q ( z ) D( z ) Q H ( z )(5)where D(z) and Q(z) are singular value matrix and the corresponding eigenvector matrix. By defining
Fw ( z ) = D −1/ 2 ( z ) Q H ( z )(6)the reference signals are whitened by convolution with Fw (z) as is shown in Figure 1(b).
Similarly, for a multichannel coupling secondary path matrix Sˆ ( z) , it can be decomposed as(7)Sˆ ( z) = U ( z) ( z)V H ( z)where U(z) and V(z) are matrices consisting of left and right singular vectors,  ( z ) is the singularvalue matrix. By defining(8)
Sˆmi ( z ) =V ( z ) + ( z)(9)Sˆ ( z) = U H ( z)aithe compensated secondary path in Figure 1 (b) is(10)Sˆ ( z) Sˆmi ( z )= U ( z ) ( z)V H ( z )V ( z ) + ( z ) = U ( z )where the superscript “+” is pseudo-inverse operation. Thus, to update the control filter, the reference
signals only need to be filtered by the reverse order of the Sˆai ( z) .

3. DECOMPOSITION OF SECONDARY PATHS
3.1

Single-channel Secondary PathA secondary path measured in a car from a headrest loudspeaker to an ear of the passenger is used
to verify the performances of the two decomposition algorithms. The responses of the secondary pathin time and frequency domain are shown in Figure 2 with a sampling frequency of 8192 Hz.

(a) The response in time domain(b) The response in frequency domain
Figure 2 – Responses of the secondary path
3.1.1 Minimum-phase/Allpass Decomposition
The decomposition results of the minimum-phase and allpass components are shown in Figure 3,
and their convolution equals the response of the secondary path, which illustrates the decomposition
results are correct. Figure 3(b) shows the frequency responses of the minimum-phase and allpass
components, and a flat response of the allpass part is observed. Thus, after decomposition andcompensation, the secondary path has a flat response in all frequency bands, which is beneficial for
active noise control systems.

(a) The result in time domain(b) The result in frequency domain
Figure 3 – Decomposition results of the minimum-phase/allpass decomposition
3.1.2 Singular Value Decomposition(a) The results in time domain(b) The results in frequency domain

Figure 4 – Decomposition results of the singular value decomposition
The singular value decomposition results of the above secondary path are shown in Figure 4, wherethe filters Sˆmi ( z ) , Sˆai ( z) and Sˆ ( z) Sˆmi ( z) are non-causal because there are large responses at the end of theseries. Although Sˆai ( z) has a flat frequency response, it can’t be used directly in time domain.
To make sure the decomposition results are causal, 25 sample delays are introduced and the results
are displayed in Figure 5. Comparing Figures 4 and 5 illustrates that the time responses of Sˆmi ( z ) andSˆai ( z ) with 25 sample delays become causal.

Figure 5 – Decomposition results with 25 sample delays
3.2 Two-channel Coupling Secondary Paths
For two-channel case, the coupling secondary paths in the Ref.[6] are used to analyze. Since thedecomposition results are same as the references, only new results are presented in the following.
Because the minimum-phase/allpass decomposition for multi-channel secondary paths is difficult, a
simple acoustic model in free field is adopted in the references, where the minimum-phase and allpass
components can be computed theoretically.
The minimum-phase/allpass decomposition result achieves the decoupling of the secondary paths,
which can be observed from its equation as z − N1
0 
Sˆall ( z ) = (11)− N1 z  0However, for the result of SVD, the decoupling of the secondary paths are not obtained. The time
responses of Sˆ ( z) Sˆmi ( z) are shown in Figure 6 and it can be seen that the coupling paths still have large
responses. The SVD only compensates each secondary path to have a flat frequency response,
including coupling secondary paths.

Figure 6 – The time responses of Sˆ ( z) Sˆmi ( z)

4. PREWHITENING OF REFERENCE SIGNALS
In this section, reference signals are prewhitened using the two methods and the results are
discussed. Since the minimum-phase/allpass decomposition for multi-reference systems is difficult,only single reference signal is processed. The sampling frequency is set to 8192Hz and a series ofpink noise is adopted as the reference signal.
4.1 Minimum-phase/Allpass Decomposition
The derived prewhitening filter is shown in Figure 7(a). Since the prewhitening filter F(z) is
minimum-phase, its inverse filter F -1 (z) can be calculated directly. It can be seen that F -1 (z) has acharacteristic like a highpass filter. Thus, after the reference signal is filtered by F -1 (z), the obtained
result has a flat response in the frequency band, as is shown in Figure 7(b).

(a) The frequency responses of F and F-1(b) The spectral density of the prewhitened signal
Figure 7 –The frequency responses of prewhitening filters and its prewhitened result
4.2 Singular Value Decomposition
The SVD process of reference signals is similar to Section 2.2 and a few sample delays have to be
introduced to make the filter causal. The derived prewhitening filters Fw (z) with 4 and 20 sample
delays are shown in Figure 8(a). Similarly, F w (z) also has the characteristics of a highpass filter.
However, there is a large difference for F w (z) with different delays in the low frequency range, which
can be noticed obviously from the power spectral density of the reference signal filtered by F w (z) as
is shown in Figure 8(b). It can be seen that the prewhitening filter F w (z) with more sample delays has
better whitening effect in the low frequency range.

(a) The time responses(b) The prewhitened reference signals
Figure 8 – The time responses of the prewhitening filters using SVD and their prewhitened results

5. SIMULATIONSIn this section, the two decomposition methods are applied to single - and two-channel coupling
secondary paths systems, respectively.
5.1 Single-channel System
A single-channel ANC system is used to verify the methods in the following, where the secondary
path and reference signal in sections 3.1 and 4 are adopted. The time response of the primary path
P(z) is shown in Figure 10.

Figure 10 – The time response of the primary path
5.1.1 With Minimum-phase/Allpass Decomposition
Based on above ANC system, the noise reductions using the FxLMS algorithm and the FxLMS
algorithm with minimum-phase/allpass decomposition are displayed in Figure 11. Figure 11(a) showsthat the FxLMS algorithm achieves a better result than FeLMS algorithm in terms of convergence rate
and noise reduction without processing the reference signal and secondary path. Figure 11(b) showsthat the FxLMS algorithm reduces the noise below 2500 Hz, while for the FeLMS algorithm, only thenoise below 1200 Hz is reduced. Thus, in the following of paper, only the FxLMS algorithm is used.

(a) The noise reduction in time domain(b) The noise reduction in frequency domain
Figure 11 – The noise reduction performance of the ANC system
After the reference signal and secondary path are processed using the minimum-phase/allpass
decomposition, the convergence rate of the algorithm is accelerated dramatically, as is shown in Figure11(a). Since the compensated secondary path has a flat frequency response, the algorithm achieves
the noise reduction in the whole frequency band.
5.1.2 Singular Value Decomposition
The noise reduction results of the algorithm with singular value decomposition are displayed in
Figure 12, where “DX” and “DG” denote the sample delay introduced for F w (z) and Sˆmi ( z ) .The noise
reduction with SVD is less than that of the original FxLMS algorithm because the sample delays are
introduced. The more sample delays, the less noise reduction is achieved. Comparing the curves“SVD(DX=5, DG=15)” and “FxLMS” shows that although a less noise reduction is derived at steadystate for the FxLMS algorithm with SVD, its convergence rate is improved.
5.2 Harmonic Noise Control for a Multi-channel System
As is analyzed in the above sections, although the minimum-phase/allpass decomposition has agreat performance, it is difficult to be applied to general multi-channel systems. While for the SVD,
since sample delays are introduced, the noise reduction performance for broadband noise is reduced,
unless the reference signals have enough time advance to the primary noise signal.
However, for the steady or slow-varying harmonic noise, since the signal is periodic, the delays
introduced by SVD can be ignored. Thus, in this subsection, the SVD is used to control the engine
noise inside a car cabin. The ANC system uses two loudspeakers of the car to control noise at twoerror microphones. The two coupling secondary paths measured in a car are shown in Figure 13.

(a) The noise reductions in time domain(b) The noise reductions in frequency domain
Figure 12 – The noise reduction performances of the ANC system

Figure 13 – The time responses of the secondary paths
The noise is recorded when the car engine is operating at 600 rpm and the 30 Hz , 60 Hz, 90 Hz,
120 Hz and 150 Hz noise components are targeted to be reduced. The reference signal containing
above harmonics is synthesized using the engine speed and all the harmonic components have same
amplitude.

(a) Noise at error microphone 1(b) Noise at error microphone 2

Figure 14 – The noise reductions of error microphones
The noise reductions at two error microphones are shown in Figure 14 and summarized in Table 1.
It can be seen that the FxLMS algorithm with SVD processing secondary paths can achieve more noise
reductions for most harmonics. This is because the secondary paths after being decomposed andcompensated have flat responses for all frequency components. Thus, a unified step size can be chosen
for the algorithm. However, it doesn’t means that the FxLMS algorithm always has a poor performance.
If each harmonic component of the synthesized reference signal has independent amplitude, a similar
result can be arrived with the FxLMS algorithm by adjusting each amplitude to a suitable value. The
FxLMS algorithm with SVD can avoid adjusting the amplitudes for harmonics.
Table 1 –Noise reductions at 2 error microphones
Components

30 Hz

60 Hz

90 Hz

120 Hz150 HzError microphones

#1

#2

#1

#2

#1

#2

#1

#2

#1

#2

FxLMS (dB)

10.1

18.0

8.5

4.3

6.0

4.3

3.1

2.0

5.4

-0.6

FxLMS-SVD (dB)

23.6

23.6

21.1

18.3

10.3

18.3

10.5

9.3

4.8

4.3

6. CONCLUSIONS
Two preconditioning FxLMS algorithms using the minimum-phase/allpass decomposition andsingular value decomposition for active noise control systems are investigated in the paper. The
decomposing results show that the minimum-phase/allpass decomposition can achieve decoupling andflatting the responses of secondary paths, and whitening reference signals. However, it is difficult tobe applied to multi-channel systems. While the singular value decomposition is easy to be popularized
and applied. But extra sample delays have to be introduced for the singular value decomposition andreference signals cannot be whiten in the low frequency range without enough sample delays. Besides,
the singular value decomposition cannot decouple secondary paths.
Simulation results show that both two preconditioning FxLMS algorithms have fast convergence
rates. Since the sample delays are introduced for the singular value decomposition, the related noise
reduction is deteriorated. Engine harmonic noise in a car isn’t sensitive to the delays, so the FxLMS
algorithm with the singular value decomposition can achieve a better performance by flatting
frequency responses of secondary paths.

REFERENCES
1. Colin H. Hansen, Scott D. Snyder, Xiaojun Qiu, Laura A. Brooks D. Active control of noise and vibration.
2ed Edition. CRC Press; 2012.
2. Krstajic B, Zecevic Z, Uskokovic Z. Increasing convergence speed of FxLMS algorithm in white noise
environment. nternational J Electron Commun. 2013;67(10):848–53.
3. Sun G, Feng T, Xu JI, Li M, Lim T. Modified FxLMS Algorithm with Equalized Convergence Speed for
Active Control of Powertrain Noise. SAE Int J Passeng Cars - Mech Syst. 2015;8(3):868–72.
4. Elliott SJ, Stothers IM, Nelson PA. A multiple error lms algorithm and its application to the active controlof sound and vibration. IEEE Trans Acoust. 1987;35(10):1423–34.
5. Kuo SM, Kong X, Chen S, Hao W. Analysis and design of narrowband active noise control systems.
ICASSP, IEEE Int Conf Acoust Speech Signal Process - Proc. 1998;6(May 2014):3557–60.
6. Elliott SJ. Optimal controllers and adaptive controllers for multichannel feedforward control of stochastic
disturbances. IEEE Trans Signal Process. 2000;48(4):10531060.
7. Elliott SJ, Cook JG. A preconditioned LMS algorithm for rapid adaptation of feedforward controllers.
ICASSP, IEEE Int Conf Acoust Speech Signal Process - Proc. 2000;2:845–8.
8. Bai MR, Elliott SJ. Preconditioning multichannel adaptive filtering algorithms using EVD- and SVDbased signal prewhitening and system decoupling. J Sound Vib. 2004;270(4–5):639–55.

ABS-0282

Modified feedback narrowband active noise control with online
secondary-path modeling
Yaping MA(1) , Yegui XIAO(2) , Liying MA(3) , Khashayar KHORASANI(3)(1) Dept. of Automation, Jiangnan University, China(2) Dept. of Information and Management System, Prefectural University of Hiroshima, Japan(3) Dept. of Electrical and Computer Engineering, Concordia University, Canada

ABSTRACT
Feedback narrowband active noise control (NANC, FBNANC) systems have been developed to suppress sinusoidal noise signals generated by rotating machines such as diesel engines, fans, etc. They do not require
any reference sensor and can avoid the frequency mismatch and the acoustic feedback, as compared with theconventional feedforward NANC (FFNANC) systems. In this paper, a modified FBNANC system is proposed
which contains three subsystems, namely: 1) a cascade pre-filtered and parallelly updated adaptive notch filterbank (CPANFB) that is included to synthesize the reference sinusoidal signals for the FBNANC controller, 2)
an online secondary-path modeling (SPM, OSPM) subsystem that is introduced into the new system to track
the secondary-path changes, and 3) a bandpass filter bank that is applied to the residual noise for separating
the remaining sinusoids from other broadband noise components, with the former utilized to scale the auxiliary
white Gaussian noise (AWGN) for the purpose of reducing its contribution to the residual noise. The three subsystems including the MPA (magnitude and phase adjuster) based controller are seamlessly integrated to work inharmony such that the whole FBNANC system enjoys nice advantages in both convergence and noise reduction
performance (NRP). Extensive simulations are conducted to demonstrate and confirm the effectiveness of the
proposed system.

Keywords: Feedback narrowband active noise control (FBNANC), adaptive notch filter bank (ANFB), online secondary-path modeling (OSPM), noise reduction performance (NRP), magnitude and phase adjuster
(MPA)

1

INTRODUCTION

Active noise control (ANC) has been widely applied to noise attenuation in various real-world applications,and it can be roughly divided into two types: the broadband ANC (BANC) and the narrowband ANC (NANC)[1]-[3]. In particular, the NANC is capable of mitigating sinusoidal noise signals generated by rotating machines
such as cutting machines, diesel engines, fans, etc.
A number of feedforward NANC (FFNANC) systems have been extensively developed [4]-[8]. They present
faster convergence, improved noise reduction performance (NRP) [4], [5], and attractive robustness against frequency mismatch (FM) [6]-[8]. However, these afore-mentioned FFNANC systems all require a reference sensor
that is used to obtain a piece of information on the target primary noise. If a reference sensor can not be placedin a proper position due to physical constraints such as high temperature, severe pollution etc., the feedback
NANC (FBNANC) will become a very promising alternative for real applications.
So far, a number of FBNANC systems have been developed and analyzed [1], [2], [9]-[15]. In [9], asimplified FBANC system is proposed that the residual noise is directly fed to the FIR controller to reduce thecomplexity due to the primary noise estimation that is involved in the conventional FBNANC, at the sacrifice of
NRP. A generalized leaky FXLMS algorithm is introduced to the FBNANC system to effectively mitigate thewaterbed effect [10]. In [11], a modified FBANC system is developed by use of an adaptive linear prediction

filter (LPF) that takes the synthetic primary signal as its input. The LPF provides a clean primary noise estimatethat is fed to the controller to improve the system NRP. A parallel adaptive line enhancer (ALE) is applied, in[12], to the estimated primary noise to generate the reference sinewaves, resulting in a less expensive and FMrobust FBNANC system. However, the online secondary-path modeling (SPM, OSPM) subsystem has been notequipped in the afore-mentioned FBNANC systems [9]-[12], that is, the secondary-path (SP) is offline estimatedin advance.
The OSPM with scaled auxiliary white Gaussian noise (AWGN) has been recently incorporated into the
FBNANC systems [13]-[15]. An appended delay is introduced to the SPM filter to monitor a variable step
size (VSS) that is used to update the SPM filter, in the hope of resolving the sluggish convergence problem in[13]. In [14], a cascade adaptive notch filter bank is adopted to extract, from the estimated primary noise, thereference sinewaves that are fed to a parallel-array of two-weight magnitude and phase adjusters (MPA) to form
the secondary source and the AWGN is simply scaled by the lowpass-filtered residual noise power. In these
OSPM-based FBANC systems [13],[14], the AWGN is indeed wisely scaled, but the OSPM and the controller
are seriously coupled. Recently, a robust narrowband FBANC system with OSPM [15] has been proposedthat presents faster convergence, improved NRP as well as nice robustness against abrupt changes with the SP
and/or the primary noise. However, it requires a long controller and a lengthy LPF-based decoupling filter as
well, significantly increasing the computational cost.
In this work, a modified FBNANC system with OSPM is proposed. First, a cascade pre-filtered and parallelly updated adaptive notch filter bank (CPANFB) [16] is included to synthesize the reference sinusoidal signals
for the FBNANC controller. Second, a bandpass filter bank (BPFB) is applied to the residual noise for separating the remaining sinusoids from other broadband noise components. Finally, an OSPM subsystem is also
introduced to track the SP. Extensive simulations with synthetic SPs and noise signals are conducted to confirm
the superiority of the proposed modified FBNANC system.

2

PROPOSED MODIFIED FBNANC SYSTEM

To overcome the drawbacks with the FBNANC system proposed in [14] and to reduce the computational
cost of a recent FBNANC that is developed in [15], a modified FBNANC system is proposed as depicted inFig. 1, where the controller is composed of q two-weight magnitude and phase adjusters (MPAs).

Figure 1. Proposed modified FBNANC system with OSPM

The new system consists of three subsystems, namely: 1) a CPANFB that synthesizes the reference sinusoids, 2) a parallel BPFB that takes the residual noise as its input to extract the remaining sinusoids from otherbroadband noise components, and 3) an OSPM subsystem for tracking the SP changes. These three subsystems including the MPA based controller are seamlessly integrated to work in harmony such that the entire
FBNANC system enjoys faster convergence as well as improved NRP in the presence of secondary-path drift
or non-stationary target noise.
2.1 CPANFB for synthesizing reference sinusoids
The primary noise is expressed byq0p(n) = p0 (n) + v p (n) = ∑i=1
Ai cos(ω p,i n + θi ) + v p (n)(1)

where Ai , ω p,i and θi denote the amplitude, angular frequency, and phase of the ith frequency component,
respectively. v p (n) is an additive white Gaussian noise with zero mean and variance σ p2 . Transfer function S(z)in Fig. 1, denotes the true SP which is usually considered as an FIR filter with order M − 1 and coefficientsM̂−1{sm }M−1
m=0 . Its estimate is expressed by Ŝn (z) owning FIR coefficients {ŝm }m=0 and order M̂ − 1. The residual
noise e(n) is expressed bye(n) = p(n) − y p (n)(2)

where y p (n) is the S(z)-filtered version of the secondary source y(n). The estimated primary noise x(n) is
achieved by
x(n) = e(n − 1) − ŷo (n − 1)(3)

where the Ŝn (z)-filtered secondary source ŷo (n) isM̂−1ŷo (n) = ∑m=0 ŝm (n)yo (n − m)(4)

and the synthetic sinusoidal secondary source yo (n) will be given later.
As depicted in Fig. 2, the CPANFB [16] is introduced to synthesize the reference sinusoids from the primarynoise estimate x(n). The CPANFB consists of 2q notch filter cells, with each implemented by a second-order
IIR notch filter that is represented by
Hi (z) =1 + ρz−1 + z−2,
1 + ρai z−1 + ρ 2 z−2

i = 1, 2, . . . , q(5)where ai (= −2 cos ωi ) is the ith frequency-related filter weight, and constant ρ(∈ [0, 1)) denotes a pole attraction
parameter which determines the notch filter bandwidth. The value of ρ is usually set very close to unit, andthus the ith ANF can almost remove a sinusoid with frequency ωi , while allowing other sinusoids to passunchanged. Note that q is no less than q0 .
The normalized gradient (NG) algorithm is used to tune the filter weight ai (n) so as to track the frequencies
within estimated primary noise signal x(n) as follows:gi (n)
ε + Gi (n)(6)

Gi (n) = β Gi (n − 1) + (1 − β )g2i (n)(7)

ai (n + 1) = ai (n) − µ1 yb,i (n)where µ1 is a positive step size, β (∈ [0, 1)) is a forgetting factor, ε is a small positive user parameter that is
introduced to avoid division by zero in the NG algorithm, the output yb,i (n) of the ith parallel ANF and gradientsignal gi (n) are respectively calculated by
yb,i (n) = −ρai (n)yb,i (n − 1) − ρ 2 yb,i (n − 2)+xd,i (n) + ai (n)xd,i (n − 1) + xd,i (n − 2)
gi (n) = −ρyb,i (n − 1) + xd,i (n − 1)

(8)
(9)

Figure 2. A CPANFB subsystem for synthesizing the reference sinusoids
whereq

xd,i (n) = x(n) − ∑k=1,k6=i yd,k (n)(10)

yd,i (n) = yc,i−1 (n) − yc,i (n)(11)
2yc,i (n) = −ρai (n)yc,i (n − 1) − ρ yc,i (n − 2)
+yc,i−1 (n) + ai (n)yc,i−1 (n − 1) + yc,i−1 (n − 2)(12)and yc,0 (n) = x(n). Note that yc,i (n) and yd,i (n) are the output and error signal of the ith cascade pre-filtered
ANF, respectively, and its ai (n) is provided by the ith parallel ANF. Eventually, the individual reference signal
for the MPAs can be expressed byxi (n) = xd,i (n) − yb,i (n).

(13)

2.2 A parallel BPFB for separating residual noise components
As shown in Fig. 3, a parallel BPFB is applied to the residual noise for separating the remaining sinusoids
from other broadband noise components. The output of the ith bandpass filter is calculated by
ub,i (n) = −ρe ai (n)ub,i (n − 1) − ρe2 ub,i (n − 2)−(1 − ρe ) [ai (n)e(n − 1) + (1 + ρe )e(n − 2)](14)

where ai (n) is provided by the CPANFB, and ub,i (n) will be used to update the controller in next subsection.

Figure 3. A parallel BPFB for separation of residual noise components
Furthermore, the remaining sinusoids is given byqub (n) = ∑i=1 ub,i (n)which is utilized to scale the AWGN v0 (n) that will be provided later.

(15)

2.3 Online SPM subsystem
An OSPM subsystem is also included in the proposed FBNANC system to ensure the stability of the entire
system in the presence of the SP drift or big changes. Transfer function S(z) denotes the true secondary path
which is usually considered as an FIR filter with order M − 1 and coefficients {sm }M−1
m=0 . The coefficients of its
estimate may be updated by the LMS algorithm as follows,ŝm (n + 1) = ŝm (n) + µs es (n)v(n − m)

(16)

where
M̂−1

es (n) = e(n) − ys (n) = e(n) − ∑m=0 ŝm (n)v(n − m)

(17)v(n) = v0 (n)Gs (n)(18)

Gs (n) = αGs (n − 1) + (1 − α)u2b (n − 1)(19)

and µs is a step size, v0 (n) is the AWGN with zero mean and variance σ02 , α is another forgetting factor, andv(n) is the scaled AWGN.
2.4 Controller based on magnitude and phase adjusters
The proposed ANC controller consists of q two-weight magnitude and phase adjuster (MPA) cells withweight set {h0,i (n), h1,i (n)}qi=1 and is utilized to synthesize the sinusoidal secondary source. The output of thecontroller is expressed byqyo (n) = ∑i=1 yi (n)(20)

yi (n) = h0,i (n)xi (n) + h1,i (n)xi (n − 1).

(21)

where

The FXLMS algorithm is designated to update the two weights of the ith MPA,h0,i (n + 1) = h0,i (n) + µ2 ub,i (n)x̂i (n)(22)

h1,i (n + 1) = h1,i (n) + µ2 ub,i (n)x̂i (n − 1)

(23)

where
M̂−1

x̂i (n) = ∑m=0 ŝm (n)xi (n − m)(24)

and µ2 is a step size. Finally, the secondary source with scaled AWGN is obtained byy(n) = yo (n) − v(n).

3

(25)

SIMULATIONSExtensive simulations with synthetic noises and typical SP settings are performed to verify the effectivenessof the proposed modified FBNANC system. Both the previous FBNANC system [14] and the proposed one
were compared here. Simulation results for two cases are provided. In Case 1, the primary noise frequencies
present sudden changes in the middle of adaption. In Case 2, the true SP presents a drift in the middle ofadaptation. Simulation conditions, user parameters as well as NRP are provided for both cases in Table 1. In
both cases, forty independent runs are conducted for statistical evaluation and comparison.
Two typical simulation results for Case 1 and Case 2 are shown in Figs. 4 and 5, respectively. From thesefigures and many other results that are not shown here due to space limitation, we have the following remarks:
1) The CPANFB could effectively extract the sinusoids that are time-varying nature (Fig. 4(c) and Fig.
5(c)). The number of active cells (q) in the ANFB is set to be larger than the number of sinusoids involved

Table 1. Simulation conditions and NRPs.
Case A
Frequency

1st half: ω p,i = {0.15π, 0.25π, 0.35π}

Case Bω p,i = {0.15π, 0.25π, 0.35π}

2nd half: ω p,i = {0.15π, 0.25π, 0.35π}
Amplitude

Ai = {1.0, 0.5, 0.25}

Ai = {1.0, 0.5, 0.25}

Phaseθi = {0, 0, 0}

θi = {0, 0, 0}

σ p2 , σo2 , α0.1, 1.0, 0.999

0.1, 1.0, 0.999

S(z)FIR: M = 21, ω = 0.50π

1st half: M = 21, ω = 0.50π

s = f ir1(M − 1, 0.5)s0 = f ir1(M − 1, 0.5)
2nd half: s1 = s0 [1 + randn(1, M) × 0.25]

Ŝn (z)M̂ = 31M̂ = 31

CPANFBρ = 0.975, β = 0.98, ε = 0.01, q = 4

ρ = 0.975, β = 0.98, ε = 0.01, q = 4

BPFB

ρe = 0.92

ρe = 0.92

Step sizes

Con: µ1 = 0.0003, µ2 = 0.01, µs = 0.0004

Con: µ1 = 0.0003, µ2 = 0.013, µs = 0.0004

Pro: µ1 = 0.0003, µ2 = 0.01, µs = 0.001

Pro: µ1 = 0.0003, µ2 = 0.013, µs = 0.001

1st half: Con: 7.62, Pro: 8.24

1st half: Con: 7.58, Pro: 8.21

2nd half: Con: 8.05, Pro: 8.31

2nd half: Con: 7.91, Pro: 8.25

NRP [dB]

Note: Con: previous FBNANC system [14]; Pro: the proposed FBNANC system.

(a) Primary noise and residual errors(b) SPM MSE(c) Filter weight of CPANFB(d) Gain scaler
Figure 4. Simulation results of Case 1

(a) Primary noise and residual errors(b) SPM MSE(c) Filter weight of CPANFB(d) SP drift
Figure 5. Simulation results of Case 2
in the primary noise. Indeed, our modified system still works well if less ANFB active cells are used. This
property is very attractive in real-life applications where the number of sinusoids may be unknown in advance.
2) The MPAs could efficiently produce the secondary source. As each MPA only has two weights, theFBANC controller is significantly smaller in size as compared to the long FIR controller that is used in previous
works [9]-[11], [15].
3) As compared with the previous FFNANC system [14], our FBNANC with OSPM can deal with therandom SP coefficient drift (Fig. 5(d)). However, if the SP variation is large or abrupt, for example, the lengthof the FIR-type SP demonstrates sudden changes, our proposed system will present very poor stability, rendering
itself useless. Therefore, developing a more robust OSPM scheme for FBNANC is an interesting future research
topic.
4) Both Figs. 4 (a) (b) and Figs. 5 (a) (b) indicate that the new system does present faster convergence rate
in terms of the residual error and the SPM MSE. As shown in Table 1, our proposed system produces relatively
larger NRP values than that of the previous system [14], though the NRP difference between the two systems
is not very significant.

4

CONCLUSIONSIn this paper, a modified FBNANC system has been proposed which contains three subsystems, namely,
the CPANFB subsystem including the MPAs, the OSPM subsystem, and the BPFB. On the one hand, theCPANFB can effectively and efficiently provide high-quality reference signal. On the other hand, the parallel
BPFB can extract the remaining sinusoids from other broadband noise components, with the former utilized
to scale the AWGN and thus leading to improved system NRP. The proposed system enjoys nice advantagesof both faster system convergence and improved NRP as compared to its counterpart. Extensive simulations
with synthetic stationary and nonstationary primary noise signals and different SP settings are conducted andprovided to demonstrate the superiority of the proposed system. Future research topics include: 1) performingin-depth analysis of the proposed system, 2) improving its robustness against abrupt SP changes, 3) applying
the proposed system to real noises and real SPs, etc.

ACKNOWLEDGEMENTS
This work was supported in part by the National Natural Science Foundation of China (62003149), in partby the Natural Science Foundation of Jiangsu Province (BK20200612), and in part by the JSPS Grant-in-Aid
for Scientific Research (C) (15K06117, 18K04175), Japan.

REFERENCES[1] S. M. Kuo and D. R. Morgan, Active Noise Control Systems - Algorithms and DSP Implementation, New
York: Wiley, 1996.
[2] S. M. Kuo and D. R. Morgan, Active noise control: A tutorail review, Proc. of the IEEE, 87 (6) (1999),
943-973.
[3] L. Lu, K. Yin, R. C. Lamare, Z. Zheng, Y. Yu, X. Yang, and B. Chen, A survey on active noise control in
the past decade-Part I: Linear systems, Signal Process., 183 (2021) 108039.
[4] C. Y. Chang and S. M. Kuo, Complete parallel narrowband active noise control systems, IEEE Trans. Audio,
Speech, Lang. Process., 21 (9) (2013), 1979-1986.
[5] Y. Ma and Y. Xiao, A new strategy for online secondary-path modeling of narrowband active noise control,
IEEE-ACM Trans. Audio, Speech, Lang. Process., 25 (2) (2017), 420-434.
[6] Y. Xiao, L. Ma, K. Khorasani, and A. Ikuta, A new robust narrowband active noise control system in thepresence of frequency mismatch, IEEE Trans. Audio, Speech, Lang. Process., 14 (6) (2006), 2189-2200.
[7] H. J. Jeon, T. G. Chang, and S. M. Kuo, Analysis of Frequency Mismatch in Narrowband Active NoiseControl, IEEE Trans. Audio, Speech, Lang. Process., 18 (6) (2010), 1632-1642.
[8] H. J. Jeon, T. G. Chang, and S. M. Kuo, A narrowband active noise control system with frequency corrector,
IEEE Trans. Audio, Speech, Lang. Process., 19 (4) (2011), 990-1002.
[9] L. Wu, X. Qiu, and Y. Guo, A simplified adaptive feedback active noise control system, Appl. Acoust., 81(2014), 40-46.
[10] L. Wu, X. Qiu, and Y. Guo, A generalized leaky FxLMS algorithm for tuning the waterbed effect offeedback active noise control systems, Mech. Syst. Signal Process., 106 (2018), 13-23.
[11] N. Miyazaki and Y. Kajikawa, Modified-error adaptive feedback active noise control system using linear
prediction filter, IEICE Trans. Fundamentals, E97-A (10) (2014), 2021-2032.
[12] C. Y. Ho, K. K. Shyu, C. Y. Chang, and S. M. Kuo, Efficient narrowband noise cancellation system using
adaptive line enhancer, IEEE-ACM Trans. Audio, Speech, Lang. Process., 28 (2020), 1094-1103.
[13] M. T. Akhtar, Narrowband feedback active noise control systems with secondary path modeling using
gain-controlled additive random noise, Digit. Signal Process., 111 (2021) 102976.
[14] X. Tan, Y. Ma, Y. Xiao, L. Ma, and K. Khorasani, A new feedback narrowband active noise control systemwith online secondary-path modeling based on adaptive notch filtering, Proc. Int. Conf. Adv. Mechatron.
Syst., 2020, pp. 78-82.
[15] Y. Ma, Y. Xiao, B. Huang, T. Bai, and X. Tan, A robust feedback active noise control system with online
secondary-path modeling, IEEE Signal Process. Lett., 29 (2022), 1042-1046.
[16] W. Wu, Y. Xiao, J. Lin, L. Ma, and K. Khorasani, An efficient filter bank structure for adaptive notch
filtering and applications, IEEE-ACM Trans. Audio, Speech, Lang. Process., 29 (2021), 3226-3241.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0520

Implementation of an active vibration control system to suppress
the transmitted traction motor vibration for reducing the motor
whine noise in an electric car cabin
Seokhoon Ryu1; Jihea Lim2; Young-Sup Lee3 Myunggyu Kim4;
1-3

Department of Embedded Systems Engineering, Incheon National University, Korea
4

Research & Development Division, Hyundai Motor Company, Korea

ABSTRACTThis study investigates the implementation of an active vibration control system to suppress the vibrationtransmitted from the traction motor of an electric car at the motor mount brackets for reducing structureborne motor whine noise in a car cabin. Motor whine noise is easily perceptible and annoying to passengers
due to its high frequencies which are closer to the sensitive range for human hearing sensation. An active
vibration control approach was considered in this study and was implemented in an electric car. A total of
two tri-axis accelerometers as error sensors were installed at the right and center motor mount brackets,
respectively, and three vibration generators as secondary actuators were installed at each mount. The realtime control experiment was carried out while the test car was accelerated from 0 to 100 kph on a paved road.
The results showed that the sound pressure level of the 24th order component at the driver’s ear wasattenuated in a range of 500 -1200 Hz.
Keywords: Motor whine noise, Active vibration control, Reduction of whine noise

1. INTRODUCTION
The motor whine noise of electric vehicles is caused by the operations of its powertrain including
the traction motor and the gearbox. This noise has high frequencies which are closer to the sensitive
range for human hearing sensation, so it can give the passengers annoying and unpleasant feelings [1].
Apart from passive control methods, active control methods can be considered to suppress the
motor whine noise inside a passenger car. However, it is difficult to directly suppress the whine noise
through the active noise control approach using loudspeakers which is known to be effective under
500 Hz [2].
As an alternative, it is possible to reduce the whine noise by suppressing motor vibrations
associated with the structure-borne component contributing to the noise with the active vibration
control (AVC) approach.
Therefore, in this study, an AVC system to suppress vibrations at motor mount brackets which aretransmitted from the traction motor was considered for reducing the structure -borne motor whine noise
in a passenger car. The proposed AVC system was implemented in an actual elec tric car and tested inreal-time while the test car was accelerated on a paved road. Then, the control experiment results wereanalyzed and discussed.

2. Active vibration control system
2.1 Control algorithm
A single-reference multiple-input multiple-output vibration control algorithm was designed to
yuzeng@inu.ac.kr
jhl@ inu.ac.kr
3
ysl@inu.ac.kr
4mgkim78@hyundai.com
1
2

suppress motor order vibrations at a motor mount bracket and it was based on adaptive narrowband
FxLMS whose update equation of the control filter can be w(n) given by [3]ˆ T (n)e(n)w(n + 1) = w(n) −  R(1)ˆ (n) and e( n) are the convergence coefficient, filtered reference signal matrix and error
where  , R
signal vector, respectively, and the superscript T indicates the transpose.

2.2 Control system set-up
The proposed AVC system was implemented in an electric vehicle. At each of the right and centermotor mount brackets, three vibration generators and one 3-axis accelerometer (356A32 PCB) were
installed. The control algorithm was embedded in a control unit (DS4014, dSPACE). The rest of thecontrol system consisted of signal conditioners (480E09, PCB), power amplifier s (Stereo Box S, ProJect) and two low-pass filters for anti-aliasing and reconstruction. The motor speed in r/min wasmeasured from CAN signal. The sampling frequency of the real-time control was 16,000 Hz. In
addition, a microphone to measure sound pressure was installed at the driver's ear location.

3. Experiment results and discussions
The real-time control experiment was carried out while the test car was rapidly accelerated from 0
to 100 kph for about 10 seconds on a paved road. During the experiment, the C24 vibration was
controlled in a range of frequencies from 500 to 1600 Hz.
Figure 2(a) shows the A-weighted sound pressure levels (SPLs) measured from the microphone atthe driver's ear before and after controls, and Figure 2(b) displays the attenuation after control. It wasobserved that the C24 whine noise was reduced in the range of 500 - 1200 Hz, though the vibration
control was applied in the range of 500 - 1600 Hz. Especially, the resonances at about 900 and 1050
Hz were suppressed by about 7 and 6 dB, respectively. These results show that the structure-borne
noise was mitigated by suppressing the related motor vibrations at motor mount brackets.

(a)(b)
Figure 2 - Control Experiment results. (a) A-weighted SPLs before and after controls. (b)Attenuations.

4. Conclusions
This paper describes the implementation and experiment results of an AVC system to suppress thevibration transmitted from the traction motor of an electric car at the motor mount brackets for
reducing structure-borne motor whine noise in a car cabin. A three-axis accelerometer and threevibration generators were installed on each of the right and center mount brackets of a test car. The
real-time control experiment was carried out while the test car was accelerated from 0 to 100 kph ona paved road. The experimental results showed that the A-weighted SPL of the C24 order at the driver's
ear was reduced by up to 7 dBA.

REFERENCES
1. David L. Thomas L. Arne N. Prominence of tones in electric vehicle interior noise, Proc Internoise 2013;15-18 September 2013; Innsbruck, Austria. p.508-515.
2. Kuo S. M., Morgan K. R. Active noise control, algorithms and DSP implements, John Wiley & Sons;
1996.
3. Elliott S. J. Signal processing for active control, Academic Press; 2001.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0680

Control engine sound for individual preferenceby active sound quality control
Kenta MURAI1; Shunsuke ISHIMITSU2
1, 2

Graduate School of Information sciences, Hiroshima City University, Japan

ABSTRACTWith current noise control, sound quality control using Active Noise Control has been used as a noise
reduction method, targeting low-frequency noise. Our previous study revealed that individual differences
affect the impression of individual sounds. Therefore, this method is difficult to apply to products that haveunified preferences. In this study, we proposed the engine sound control system adapted to each subject's
preference. As a proposed algorithm, we adopted active sound quality control which amplifies and reduces
the frequency peculiar to the engine by applying ANC. Targeted engine sounds were selected based on theindividual’s preferred sound when connected to their driving pattern. From the result of this categorization,
we performed auditory tests to conform to each subject’s preference and determined the sound characterizedby each individual’s preference. Self-organization maps were used to identify the individual favorite pattern,
and the control signal was transmitted to the ANC system. As a result, we produced the active sound quality
control system, which allows automatic generation of the preferred sound quality of each individual.
Keywords: Sound Quality Control, ANC

1. INTRODUCTION
Active noise control (ANC) [1] has received attention as a noise reduction method. ANC reduces
noise by superimposing on a target a sound with the same amplitude but opposite phase. ANC
technology has several advantages. First, ANC technology is effective in removing low -frequency
noise that is difficult to reduce through conventional passive reduction methods such as the applicatio nof sound-insulating material, soundproof material, or damping material. Second, ANC technology canbe implemented in a smaller space than that required by conventiona l passive reduction methods.
Therefore, ANC technology is currently used to reduce vehicle interior noise [2] [3]. However, driving
a car can be considered a leisure activity [4], and a reduction in the noise level can reduce the drivi ng
pleasure, the fun of driving, or the ‘sporty’ feeling, especially for automobiles. The control of engine
sound thus shifts from noise reduction to sound design [5]. Many manufacturers have actively studied
such sound design. Active sound quality control (ASQC) technology ba sed on ANC technology has
been proposed for engine sound design [6]. In this paper, we propose an ASQC method for designingengine sound. Specifically, we propose an algorithm that amplifies and reduces the engine soundcomponents of specific orders simultaneously.

2. Proposal of Noise Control by Multiple Error Command LMS Algorithm
2.1 Proposed Algorithm
Figure 1 is a block diagram of the proposed algorithm. The algorithm amplifies the first -ordercomponent of the engine sound and reduces the second-order component. In Fig. 1, x(n) is thereference signal (generated from the ignition trigger pulse), y(n) is the control signal, d(n) is thedesired signal, e(n) is the error signal, W is an adaptive filter, e'(n) is the pseudo -error signal, and c(n)is the command signal, where the suffix indicates the order. G is the secondary path (between sensor
and actuator) and 𝐺̂ is the model of the secondary path. For this algorithm, a sine wave corresponding
to the order of the engine sound is input as the reference signal x(n ). It is possible to set the adaptive
filter for each order because the convergence coefficient can be set to each order. The algorithm is1
2

murai@sd.info.hiroshima-cu.ac.jp
ishimitu@hiroshima-cu.ac.jp

thus expected to improve the convergence property for fluctuating sound.
𝑒1′ (𝑛) = 𝑒(𝑛) − 𝑐1 (𝑛)(1)The adaptive filter W (with filter length 𝑁𝑊 ) is then expressed by equation (2), where μ is theconvergence coefficient.
W(n) = [𝑊0 (𝑛), 𝑊1 (𝑛 − 1), ⋯ , 𝑊𝑁𝑤−1 (𝑛)](2)
The adaptive filter that reduces the pseudo-error signal is then expressed by equation (3).
𝑊1 (𝑛 + 1) = 𝑊1 (𝑛) − 𝜇𝑒1′ (𝑛)𝑟(𝑛)(3)𝑊2 (𝑛 + 1) = 𝑊2 (𝑛) − 𝜇𝑒(𝑛)𝑟(𝑛)(4)Here, r(n) is the filtered reference signal (equation (5)).
r(n) = [𝑟(𝑛), 𝑟(𝑛 − 1), … , 𝑟(𝑛 − 𝑁𝑊 + 1)](5)

The proposed algorithm is a control system of a single point. Because its quiet zone is narrow, a multi input, multi-output system is required.

Figure 1 – Block diagram of the proposed algorithm.

Figure 2 – Block diagram of the expanded algorithm.
Therefore, the proposed algorithm shown in Figure 1 is expanded to multiple inputs and multiple
outputs using the multiple-error filtered-x least-mean-square algorithm to allow expansion of the quiet

zone [7]. The expanded multi-input, multi-output algorithm is shown in Figure 2. The figure is a block
diagram for the case of two reference signals, two secondary sources, and two error sensors. In the
figure, x(n) is the reference signal (generated from the ignition trigger pulse), y(n) is the control signal,d(n) is the desired signal, e(n) is the error signal, W is an adaptive filter, 𝑒 ′ (𝑛) is the pseudo-error
signal, c(n) is the command signal, G is the secondary path (between sensors and actuators), and 𝐺̂ isthe model of the secondary path. Furthermore, the subscript l in 𝑑1 , 𝑒1 , and 𝑒1′ denotes the error
sensor, the subscript s in 𝑥𝑠 (𝑛) and 𝐶𝑠 (n) denotes the reference signal, and 𝑤𝑚𝑘 is the k-th orderadaptive filter corresponding to secondary source m.
The present study used an automotive with a four-cylinder four-cycle engine. The engine sound
was recorded via a microphone (MI-1431, Ono Sokki Co., Ltd., Japan) at a sampling frequency of
8120 Hz. The experiment using DSP was performed in a simulation system. A sensor was installed in
the control point, and a control sound was outputted from an actuator (KFCRS170, KENWOOD Co.,
Ltd., Japan) to control the engine sound outputted from the noise source (S -ST5-LR, Pioneer Co., Ltd.,
Japan). The driving conditions were steady-state operation at 3000 rpm.
In the experiment, the proposed algorithm was used with an ignition trigger pulse and the engine
sound. The convergence coefficient was set appropriately. The target frequencies were the engine
sound's second-, third-, and fourth-order components. This control aimed to amplify the second-ordercomponent and reduce the third- and fourth-order components to investigate its control performance
because the active reduction for higher components is more complicated than the control for lower
components. The reference signal x(n) was used for each of the second -, third-, and fourth-ordercomponents. The desired signal d(n) was the engine sound. The command signal was the second -ordercomponent of the engine sound at the control point.
2.2 Noise Control result by proposed algorithm
Figure 3 shows the experimental results for steady-state operation. The solid line shows the state
before control, while the broken line shows the state after control. These results were obtained byaveraging over 10 seconds and applying Z weighting. Table 1 confirms an amplification of 12 dB for
the second-order component (100 Hz). Additionally, a reduction of 14 dB for the third -ordercomponent (150 Hz) and an amplification of 12 dB for the fourth-order component (200 Hz) was
found. Table 1 gives the reduction and amplification rates (where a negative value indicates reduction
and a positive value amplification) for each frequency achieved through the control. In Fig. 3, theamplification and reduction of engine sound of specific order components by the proposed algorithm
are confirmed for steady-state operation.
From Figure 3, the engine-specific order components’ amplification and reduction are confirmedwith the proposed algorithm.

Figure 3 – Experimental result in steady state operation.

Table 1 – Reduction and the amplification at each frequency (steady state operation).
Frequency
100Hz
150Hz
200Hz
Reduction and
+12dB
-14dB
-12dB
Amplification rate
As a result, it was possible to control the engine sound like an audio equalizer. Additionally, it ispossible to obtain a reference signal from the ignition trigger pulse signal, which enables robust
control against disturbances such as road noise. As it is possible to set a convergence coefficient foreach order component, we suggest that the convergence property can also be improved.
Figure 4 is a spectrogram of the simulation results for acceleration. Figure 4(a) presents thesimulation results before control, while Figure 4(b) presents the simulation results after control. The
figure confirms the amplification reduction of the second-order component, amplification of the thirdorder component, and amplification of the fourth-order component. In this case, the control was
focused on ‘sporty feeling’, constructed with the reduction of second-order component and theamplification of the higher components [8].
Moreover, three order components were controlled in the present study, and future implementationsof the system will increase the number of order components. We expect a more exact sound design tobe achieved by increasing the number of controlled order components.

(a) Before control(b) After control
Figure 4 – Experimental result in acceleration operation

3. Subjective Preference Measurement for Engine Sound
3.1 Auditory impression experiment contents
The amplitude of the reference sound was adjusted to make the A -weighted sound pressure level
equal to the level of the recorded real engine sound. Then, one of the following actions was performedon these stimuli. Control order components were set at first second -order components, and both firstand second-order components and levels of amplification or reduction were set at 10 or 20 dB,
respectively. These higher harmonics constitute the main components of sound and noise. Tenvolunteers (22–23 years old; seven men, three women) with normal hearing participated in thisexperiment. They were seated in an anechoic room with a comfortable therma l environment. Scheffe’spaired-comparison tests [9] were performed for all combinations of the pairs of stimulus for eachreference noise, i.e., 78 pairs (N [N – 1] / 2, N = 13) of stimuli with a different order of each pair per
session, and random presentation of the pairs. Each pair of stimuli was presented four times todetermine the preference scale value. And participants were asked to judge their preferred engine
sound to create a scaled preference value on a scale of −3 to 3. The scale values of the preference
were calculated according to Scheffe’s theory.
3.2 Experiment results
Figure 5 shows the relationship between the order components and reduction levels of active soundquality control and the scale values of the preference. The horizontal axis sho ws the intensity of thefirst order component and the intensity of the second order component. In the case of only the firstor second-order component, participants gave the same scale value of preference of reference sound.
The preference levels for each stimulus were not significantly different. However, in the case of both
first- and second-order components, the preference was increased for almost every participant. The
reason for this may be that the decrease in sound pressure becomes conspicuous [10]. Figure 6 shows
the relationship between the order components and amplification levels of active sound quality control
and the scale values of the preference. The amplification level increased, and preference decreased
from the reference sound for almost every participant. The reason for this may be that the reference
sound pressure was felt to be sufficiently high. These results indicate that control corresponding to
the individual's preferences is essential for improvements in auditory impressions.

Figure 5 – Control corresponding to the individual's preferences is essential for improvements in auditory

impressions.
Figure 6 – Scale values of preference and order components and amplification levels of active soundquality control.

4. Sound Quality Control for Individual Preference
4.1 Proposed algorithm for individual preference
Figure 7 shows the ASQC algorithm adapting to individual preferences. It is based on the harmoniccommand filtered-x LMS algorithm [3]. x(n) is the input signal, e(n) is the error signal, c(n) is thecontrol signal, and W is an adaptive filter. To adapt to individual preferences from individual features,such as driving patterns, acceleration, and speed, a control signal c(n) could be created by the output
of a DNN (Deep Neural Network). In this case, the inputs of the DNN are the subject’s acceleration
patterns and outputs are a command signal for controlling the sound quality to adjust to theindividual’s preference.

Figure 7 – Expanded algorithm for Individual preference.
4.2 Sound quality control according to individual preferenceFirst, we conducted a questionnaire about sound and driving preferences with participants inadvance. From the questionnaire results, we decided on five recording points as characteristics thatshowed significant differences in each subject. They were seat vibration, speed, accelerator opening,
engine sound, and ignition pulse. Twelve frequent drivers (12 males aged 20 to 40, driving experience
3 to 28 years) participated in the study and performed in both typical and speeding situations as driving
patterns. For the experimental conditions, they were required to accelerate up to approximately 100
km/h and maintain a steady state operation for 5 s after attaining 100 km/h. Gear changes after
acceleration were set free. Since the differences in the driving patterns for each subject wereremarkably clear, the urgency driving pattern was taken as the input parameter for SOM (self organizing maps) of the DNN. Figure 8 shows the clustered result using SOM. The feat ure indexes ofeach participant were plotted on the map in four groups. From this result, an auditory experiment wasalso conducted to find the preference tendency of participants. Three types of controls were prepared
for the engine sound:
1. 20 dB amplification for first and second-order components
2. 20 dB reduction for first and second-order component reduction
3. No control
Subsequently, the sound preference of each subject was approximately divided into three classes, as
shown in Figure 9. As this result corresponded to the SOM's driving pattern, the CLMS algorithm'scommand signal could be estimated using individual driving patterns.

Figure 8 – SOM of driving pattern.

Figure 9 – SOM of individual preference.

5. CONCLUSIONSThe present study proposed an algorithm that controls engine sound components of specific orderusing ASQC technology. Results of an experiment using DSP confirmed the amplification andreduction of components of engine sounds of specific orders via the proposed algorithm. However,limited space in an actual vehicle will reduce the reduction and amplification control rates. The
proposed algorithm was expanded to multiple inputs and multiple outputs so that it could be adopted
for expansion of quiet zone. Additional challenges are the estimated error included in the secondary
path, and the low-frequency output to be used in the control. In the subjective preference measures,
when the reduction level increased, the preference was increased from the reference s ound for almost
all participants. This may be because participants could identify a decrease in sound pressure level.
Furthermore, when the amplification level increased, the preference was decreased from the reference
sound, likely because reference sound pressure was felt to be sufficiently high. These results indicatethat control corresponding to the individual's preferences is essential for improvements in auditory
impressions. Finally, these results were combined using DNN. A novel ASQC method has bee nproposed, and the applicability of ASQC in estimating individual preference has been shown. In future
work, we will improve the robustness of the proposed algorithm and apply it to an actual automotive.

ACKNOWLEDGEMENTS
I would like to thank the engineers working for Suzuki Motor Corporation for their valuable
discussions and outstanding support for recording engine sounds.

REFERENCES
1. M. Nishimura, T. Usagawa, S. Ise, Active Noise Control, Corona Publishing Co., LTD, (2006).
2. M. Nishi, D. Ochi, Y. Nakaji, H. Nagai, M. Mizuochi, H. Mineura, "Development of ANC technology forreconciling acceleration sound with fuel economy and quietness", SAE of JAPAN 63-10 No. 20105357,
pp.7-10, (2010).
3. T. Inoue, "Active Noise Control Technology in Automobiles", Journal of the Society of Instrument andControl Engineers, Vol. 51, No. 12, (2012).
4. S. Saito, R. Yoshizaki, and R. Hayama, "A technical trend of comfortable safe car development", The
TRC NEWS No.108, (2009).
5. T. Toi, "Advice and instructions of comfortable sound design", Mechanical design, Vol. 48, No. 2, pp. 3645, (2004).
6. L. E. Rees and S. J. Elliott, “LMS-Based Algorithms for Automobile Engine Sound Profiling”, Proceedingsof 32nd International Congress and Exposition on Noise Control Engineering, pp. 1026-1033, Jeju, South
Korea, 26-28 August, (2003).
7. T. Sagawa, S. Ishimitsu, A. Yamamoto, Y. Aramaki, T. Ito K. Namekawa, T. Takagi, T. Chino, K. Yoshida
and K. Suzuki, “Study on Multichannel Active Sound Quality Control paid attention to order components”,
RISP International Workshop on Nonlinear Circuits, Communications and Signal Processing 2016, 8PM,
pp.471-474, Honolulu, Hawaii, USA, (2016).
8. N. Shibatani, S. Ishimitsu, M. Yamamoto, “Study of sound quality control of engine noise and its
evaluation”, Proceedings of internoise 2016 No.374 pp.558-565, Hamburg, Germany, (2016).
9. H. Scheffe, “An analysis of variance for paired comparisons”, Journal of American Statistical Association,
47, 381-400, (1952).
10. T. Ito, S. Ishimitsu, S. Nakagawa, “Effects of active noise control on subjective annoyance and corticalneural activities for car engine noise”, Proceedings of 43rd International Congress on Noise Control
Engineering, No.734, 7 pages, Melbourne, Australia, (2014).

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0963

A database for active control of road noise in automobile cabins
Ziyi Yang1, Youfan Wang1, Xu Zhong1,2, Jiancheng Tao1,*, Li Shi1, Haishan Zou1, Sheng Wu2, Xiaojun
Qiu2
1

Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing, 210093, China
2

Shanghai Huawei Technologies Co., Ltd., Shanghai, China

ABSTRACTThe investigation of active road noise cancellation (RNC) was started nearly 30 years ago and commercial
products have been released in recent years. In the implementation, both the noise reduction and theconvergence speed are essential in the performance assessment for adaptive algorithms. In this paper, thehistory of RNC investigation is briefly reviewed, and a database consisting of recorded signals from anelectric car is presented for researchers to test or develop different adaptive algorithms for RNC. The database
contains the primary noise at the two ears of a dummy head, 16-channel vibration reference signals at 5
different driving speeds from 50 km/h to 120 km/h, and the secondary path modelling signals of 2
loudspeakers on the shoulders of a car seat.
Keywords: Active noise control; Database; Automobile road noise

1. INRTRODUCTION
Applications of active noise control on road vehicles has been extensively investigated since 1980s
and a variety of systems have been proposed on both engine and road noise control (1). Considering
the control robustness and the feedback of the secondary source, feedforward systems with vibr ationalreference signals are preferred (2-5). The selection of the reference signals has attracted muchattentions in RNC system design (6-8). For example, 4 reference signals were selected from 16
candidate positions of a suspension system, and about 6 dB noise reduction was obtained in thefrequency band around 250 Hz when a car was driven at 60 km/h on rough asphalt and turtle -backroads (8).
The first commercial active road noise control system was released by Honda for their Accord
wagon car in 2001, where the 40 Hz narrow-band boom noise at the front seats was reduced by about
10 dB (9). In recent years, several companies introduced their road noise active control technologies
and commercial products (10-14). For example, BOSE proposed its road noise control system in 2019(10) and implemented their system based on the vehicle’s existing sound system on Tesla Model 3 incooperation with DSP Concepts in 2020 (11).
The convergence speed of the traditional Filtered-x LMS algorithm becomes slow as the numberof reference signal increases. A preconditioned LMS (PLMS) algorithm was investigated to increase
the convergence speed by decoupling the secondary path response and equalizing the signal amplitude(15). An eigenvalue equalization Filtered-x LMS (EE-FXLMS) algorithm was developed to adjust themagnitude coefficients of the estimated secondary path (16). A subband filtered -reference LMS
algorithm (SFXLMS) was also proposed, which achieved 4 dB larger attenuation between 300 and
360 Hz after applying optimal convergence factors to the decomposed frequency bands (4). A multi reference adaptive algorithm with fast convergence speed is still required in the RNC implementation
for better tracking performance.
To help researchers to test and develop adaptive algorithms for active control of road noise, adatabase measured in an electric car at 5 different vehicle speeds is reported in this paper, and thesimulation results with the standard Filtered-x LMS algorithm are presented as an example andbenchmark. It is hoped that algorithms which have rapid convergence speed and low computation load
* Correspondence should be addressed to Jiancheng Tao (jctao@nju.edu.cn)

can be developed for reducing automobile road noise.

2. DATABASE DESCRIPTION
A typical 5-seat electric car was chosen in the measurement. Two condenser microphones (lab elled
as M1 and M2) with sensitivity of 30.0 mV/Pa and 36.1 mV/Pa, respectively were placed at both earsof a dummy head in the front passenger seat to measure the primary noise and error signals. Sixteen
vibration signals were measured as reference signals and 2 loudspeakers (labelled as S1 and S2) on
the shoulder of the car seat were used as secondary sources. The arrangements of the loudspeakers
and the microphones are shown in Figure 1. During the measurement, the sampling rate was set as 16
kHz. The primary noise and vibration signals were recorded simultaneously when the car was driven
in the cruise mode at 5 different speeds of 50 km/h, 60 km/h, 80 km/h, 100 km/h, and 120 km/h.

(a)

(b)

Figure 1 – Arrangement of the loudspeakers and the microphones (a) sketch (b) photo
Table 1 – Information of the recorded data
File name

Channels setup

Experiment setup

Data length

Drive at 50 km/h

20 minDrive at 60 km/h

20 minDrive at 80 km/h

20 minPrimary_100kph

Drive at 100 km/h

20 minPrimary_120kph

Drive at 120 km/h

20 minSpeaker S1 on, vehicle not started

60 s

Speaker S2 on, vehicle not started

60 s

Primary_50kph
Primary_60kph
Primary_80kph

Secondary_left
Secondary_right

16 vibration
signals and 2
primary noise
signals

1 modelling signal
and 2 response
signals

The files named “Primary_xxkph” consist of 18 signal channels. The first 16 channels are vibration
signals and the 17th and 18th channels are the sound pressure signal obtained at M1 and M2
respectively. The modelling signals for the secondary paths were recorded when the car was turned
off. In the file named “Secondary_left” or “Secondary_right”, there are 3 signal channels. The firstchannel is the white noise signal filtered by a 1.6 kHz low passing filter, and the last two channels are
the sound pressure responses at M1 and M2 when the first channel signal is fed to loudspeaker S1 or
S2. All the recorded data were exported as 32 bit .wav files, and the detailed information is listed inTable 1. The database is free and can be downloaded from a server of Nanjing University.
(https://box.nju.edu.cn/published/rnc-data/)

3. EXAMPLES FOR USING THE DATABASE
The noise reduction performance by using the classical FxLMS algorithm based on the databasementioned above is presented in this section to help researchers to use the database correctly. In thefollowing simulations, the sampling rate is reduced from 16 kHz to 4 kHz and all the 16 vibration
signals are adopted as the reference signals. Considering the paper length requirement, only thesimulation figures at the speed of 50 km/h are presented unless otherwise specified.
3.1 Single Channel System Simulation
Loudspeaker S1 on the left shoulder of the car seat was used to reduce the sound pressure at
microphone M1, which was placed near the left ear of the dummy head. The FIR filter length was set
as 512 in both the secondary path modelling and the control filter calculation. The step sizes were
carefully selected to make the mean square error converge as fast as possible and listed in Table 2.
Table 2 – Step sizes used at different speeds in single system channel simulation
Vehicle speed

50 km/h

60 km/h

80 km/h

100 km/h

120 km/h

Step size

1.8

0.60

0.30

0.05

0.01

The sound pressure level (SPL) and A-weighted SPL between 20 to 2000 Hz at M1 without andwith control are shown in Figure 2(a) and Figure 2(b), respectively. The results were calculated byusing the recording data in the last one minute. For comparison, the simulation results obtained with
the Wiener solution with a regularization factor of 0.01 is also presented. The noise reduction indifferent frequency ranges at M1 is shown in Table 3.
Table 3 – Simulated noise reduction at M1 in a single channel system
Noise reduction

50 km/h

60 km/h

80 km/h

100 km/h

120 km/h

50~500 Hz
(dB)

FxLMS

10.6

9.4

9.2

5.6

4.0

Wiener

12.1

10.5

10.5

6.7

5.0

20~2000 Hz
(dBA)

FxLMS

9.8

11.5

9.3

6.7

5.1

Wiener

10.6

11.9

10.2

7.1

5.5

The mean square error (MSE) calculated from 20 to 2000 Hz with a step size of 1.8 is shown in
Figure 3(a) where the vehicle speed was 50 km/h. To eliminate the effect of the impact signals in therecorded data, the convergence of normalized mean square A-weighted error by using a median-filter
with 10000 points is shown in Figure 3(b). The MSE begins to converge after about 500 s, and thefinal noise reduction is about 10 dBA.

(a)

(b)

Figure 2 – Sound pressure level at M1 with the speed of 50 km/h in single channel system simulation (a)without weighting (b) with A-weighting

(a)

(b)

Figure 3 – Convergence of mean square error (MSE) at M1 at a speed of 50 km/h in a single channel
system simulation (a) MSE without post processing (b) normalized MSE with smoothing and A-weighting

3.2 Two Channel System Simulation
Both loudspeaker S1 and S2 on the shoulders of the car seat were used to reduce the squared soundpressure at the microphone M1 and M2, which were placed near the ears of the dummy head. The FIR
filter length was set as 512 in both the secondary path modelling filters and the control filters. The
step sizes adopted in the simulation at different speeds are listed in Table 4.
Table 4 – Step sizes used at different speeds in two channel system simulation
Vehicle speed

50 km/h

60 km/h

80 km/h

100 km/h

120 km/h

Step size

0.60

0.45

0.12

0.05

0.02

The sound pressure level (SPL) and A-weighted SPL from 20 Hz to 2000 Hz at M1 and M2 without
and with control are shown in Figure 4 and Figure 5, respectively. The noise reduction at different
speeds and in different statistical frequency ranges is shown in Table 5. The noise reduction and soundpressure levels are statistical values of the last minute recording data.
The mean square error (MSE) in the 2 channel system is the sum of the squared sound pressure at
the microphone M1 and M2, and the MSE calculated from 20 Hz to 2000 Hz with a step size of 0.6 isshown in Figure 6(a) for 50 km/h. The convergence of the normalized mean square A-weighted error
is shown in Figure 6(b) where the MSE convergence curve is smoothed in the same way as describedin Section 3.1. The MSE begins to converge after 700s and the noise reduction is also about 8 dBA.

(a)

(b)

Figure 4 – Sound pressure level at the speed of 50 km/h in two channel simulation (a) M1 (b) M2

(a)

(b)

Figure 5 – A-weighted sound pressure level at the speed of 50 km/h in two channel system simulation (a)M1 (b) M2
Table 5 – Simulated noise reduction in two channel system simulation
Noise reduction
M1, 50 ~ 500
Hz (dB)M1, 20 ~ 2000
Hz (dBA)M2, 50 ~ 500
Hz (dB)M2, 20 ~ 2000
Hz (dBA)

50 km/h

60 km/h

80 km/h

100 km/h

120 km/h

FxLMS

9.9

9.1

9.0

5.9

4.0

Wiener

11.9

10.4

10.5

6.7

5.0

FxLMS

9.3

10.9

8.9

6.5

4.9

Wiener

10.1

11.5

10.0

6.8

5.3

FxLMS

10.4

8.6

7.3

6.0

3.7

Wiener

12.6

10.0

9.0

7.1

4.9

FxLMS

11.4

10.1

7.2

6.7

4.6

Wiener

12.6

11.1

8.7

7.4

5.5

(a)

(b)

Figure 6 – Convergence of the mean square error (MSE) at a speed of 50 km/h in two channel systemsimulation (a) MSE without post processing (b) normalized MSE with smoothing and A-weighting

4. CONCLUSIONS
A database for active control of automobile road noise at 5 different speeds is introduced, whichcontains the primary noise around both ears of a dummy head at a passenger seat, 16 vibrationreference signals on the vehicle’s suspension and bodywork, and the modelling signals of thesecondary paths. For demonstration purpose, the noise reduction performance of the standard single channel and two-channel FxLMS algorithms based on this database is presented. Researchers areencouraged to send their algorithms to the authors to share with the communities if the performanceof their algorithm are better than that published in this paper and in the website in the future. Besides,
we would also like to increase the size of the database by adding the measurement data withauthorization from other sources and to maintain the database for public use to improve theperformance of active control systems on road noise in automobile cabins.

ACKNOWLEDGEMENTS
This work was supported by the National Natural Science Foundation of China (11874218) and
Shanghai Huawei Technologies Co. Ltd.

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1. Sutton T, Elliott S, McDonald A, Saunders T. Active control of road noise inside vehicles. Noise Control
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2. Elliott S, Sutton T. Performance of feedforward and feedback systems for active control. IEEE Trans
Speech Audio Process. 1996;4(3):214-23.
3. Akhtar M, Mitsuhashi W. Improving performance of hybrid active noise control systems for uncorrelated
narrowband disturbances. IEEE Trans Audio Speech Language Process. 2011;19(7):2058-66.
4. Duan J, Li M, Lim T, Lee M, Cheng M, Vanhaaften W, et al. Combined feedforward–feedback active
control of road noise inside a vehicle cabin. J Vib Acoust. 2014;136(4): 041020.
5. Wu L, Qiu X, Burnett I, Guo Y. Decoupling feedforward and feedback structures in hybrid active noise
control systems for uncorrelated narrowband disturbances. J Sound Vib. 2015;350:1-10.
6. Heatwole C, Bernhard R. Reference transducer selection for active control of structure-borne road noise
in automobile interiors. Noise Control Eng J. 1996;44(1):35-43.
7. Elliott S. Signal processing for active control: Elsevier; 2000.
8. Oh S, Kim H, Park Y. Active control of road booming noise in automotive interiors. J Acoust Soc Am.
2002;111(1):180-188.
9. Sano H, Inoue T, Takahashi A, Terai K, Nakamura Y. Active control system for low-frequency road noise
combined with an audio system. IEEE Trans Speech Audio Process. 2001;9(7):755-763.
10. https://www.bose.com/en_us/pressroom/archive/2019/bose-introduces-quietcomfort-road-noise-control.html, (last visited on April 21, 2022).
11. https://www.teslarati.com/tesla-cabin-insulation-bose-road-noise-control-upgrade/, (last visited on April
21, 2022).
12. https://news.harman.com/releases/releases-20200130, (last visited on April 21, 2022).
13. https://group-media.mercedes-benz.com/marsMediaSite/en/instance/ko/Under-the-microscope-Activeroad-noise-compensation.xhtml?oid=48161321, (last visited on April 21, 2022).
14. https://www.silentium.com/automotive-2/, (last visited on April 21, 2022).
15.Elliott S, Cook J, editors. A preconditioned LMS algorithm for rapid adaptation of feedforward controllers.
2000 IEEE Int Conf Acoust Speech Signal Process; 5-9 June 2000; Istanbul, Turkey. 2000. p. 845-848.
16. Thomas J, Lovstedt S, Blotter J, Sommerfeldt S. Eigenvalue equalization filtered-x (EE-FXLMS)
algorithm applied to the active minimization of tractor noise in a mock cabin. Noise Control Eng J.
2008;56(1):25-34.

ABS-0558

Implementation of Multi-channel Active Noise Control based on
Back-propagation Mechanism
Zhengding LUO, Dongyuan SHI, Junwei JI, Woon-Seng GAN
School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore

ABSTRACT
Active noise control (ANC) systems can efficiently attenuate low-frequency noises by introducing anti-noises tocombine with the unwanted noises. In ANC systems, the filtered-x least mean square (FxLMS) and filtered-X
normalized least-mean-square (FxNLMS) algorithm are well-known algorithms for adaptively adjusting control filters. Multi-channel ANC systems are typically required to attenuate unwanted noises in a large space.
However, open-source implementations of the multi-channel FxLMS (McFxLMS) and multi-channel FxNLMS(McFxNLMS) algorithm continue to be scarce. Therefore, this paper proposes a simple and effective implementation approach of the McFxLMS and McFxNLMS algorithm. Motivated by the back-propagation processduring neural network training, the McFxLMS and McFxNLMS algorithm can be implemented via automatic
derivation mechanism. We implemented the two algorithms using the automatic derivation mechanism in PyTorch and made the source code available on GitHub. This implementation method can improve the practicalityof multi-channel ANC systems, which is expected to be widely used in ANC applications.

Keywords: Active noise control, Multi-channel ANC, Implementation of McFxLMS and McFxNLMS

1

INTRODUCTION

Passive noise control techniques such as enclosures, barriers, and silencers are difficult to suppress undesired
noises at low frequencies (1). An active noise control (ANC) system is achieved by introducing a canceling“anti-noise” wave through an appropriate array of secondary sources (2). The anti-noise is of equal amplitude
and opposite phase compared to the disturbance (3). In practice, ANC systems can efficiently attenuate lowfrequency noises, whereas passive methods are either ineffective or tend to be very expensive or bulky (4).
Therefore, ANC techniques have been widely employed in some commercial products including headphones,
mobile phones and automobiles etc.
However, there is a performance degradation of single-channel ANC systems in spatial noise environments(5). In such scenarios, multi-channel ANC systems with multiple controllers, loudspeakers and microphones canbe introduced to improve the noise reduction performance (6). Some of the best-known applications are thecontrol of exhaust boom noises in automobiles (7), earth-moving machines (8), and the control of propellerinduced noises in flight cabin interiors (9). Other noise control applications like vibration control in complex
mechanical structures also require multiple channels (10).
A general multiple-channel ANC system is shown in Figure 1, which consists of J reference microphones, K
canceling loudspeakers, and M error microphones. In the system, the active noise controller is updated based on
the reference signals and error signals, sensed by the reference microphones and error microphones respectively,
so that the generated anti-noise can suppress the disturbance at the error microphones. The coefficients of ANC
controllers can be updated through adaptive algorithms to minimize the sum of the error signals (11).
Adaptive algorithms such as the filtered-x least mean square (FxLMS) (12) and filtered-X normalized leastmean-square (FxNLMS) (13) are commonly used ANC algorithms. Nevertheless, the adaptive optimization ofcontrol filter coefficients in multi-channel ANC systems is difficult to implement in practice (14). It must take
into account the interactions between all microphones and loudspeakers to provide the optimal cancelling signals(15). Compared with single-channel ANC systems, making iterative changes to the control filter coefficients
becomes much more complex in multi-channel ANC systems.

Figure 1. Block diagram of a J × K × M multi-channel ANC system using the McFxLMS algorithm.

Figure 2. The forward propagation of the McFxLMS algorithm.
Due to the difficulty of implementation, open-source codes of the multi-channel FxLMS (McFxLMS) andmulti-channel FxNLMS (McFxNLMS) algorithm are still lacking (16). To tackle the limitation, the McFxLMS
and McFxNLMS algorithm are implemented via the automatic derivation mechanism in this paper. Since
the automatic derivation can update weights given a loss function, the back propagation of McFxLMS andMcFxNLMS can be automatically achieved without resorting to extra-human efforts. The implementation codeis based on the PyTorch tool (17) and available at GitHub website. Owing to the simple implementation method,changing the number of microphones and loudspeakers in multiple-channel ANC systems is more convenient,so that the practicality is improved.

2

FORWARD PROPAGATION AND BACK PROPAGATIONA feedforward multiple-channel ANC system using the McFxLMS algorithm is illustrated in Figure 1. The
McFxLMS algorithm is used to update the active noise controller. The J × K × M multiple-channel ANC system
includes J reference microphones, K canceling loudspeakers, and M error microphones. For the purpose of
easily implementing adaptive algorithms in PyTorch, we split the adaptive process into two phases: forward
propagation and back propagation. Then, the McFxLMS algorithm is described in detail as an example.
2.1 Forward propagation
In forward propagation, as shown in Figure 2, the input component of the McFxLMS algorithm at its n-th
iteration is the reference vector X(n) given byhiT
X(n) = xT1 (n) · · · xT j (n) · · · xT J (n) ∈ RJN×1 ,(1)

where T denotes the transpose operation. The control filter length is N taps. The reference signal vector picked
up by the j-th microphone can be expressed ashiTx j (n) = x j (n) x j (n − 1) · · · x j (n − N + 1) ∈ RN×1 .
(2)
The control filter matrix is represented aswT (n)
 11
 T
w21 (n)W(n) = 
 ..
 .

wTK1



···

wT1J (n)

···
..
.



wT2J (n) 
K×JN,..  ∈ R. 
wTKJ (n)···(3)

The element wk j (n) in control filter matrix means the control filter from the jth reference to the kth output andcan be denoted as
h
iT
(2)
(N)
wk j (n) = w(1)
∈ RN×1 .
(4)
(n)
w
(n)
·
·
·
w
(n)
kj
kj
kj
Hence, the control signal y(n) can be obtained fromy(n) = W(n)X(n) ∈ RK×1 ,

(5)

h
i
y(n) = y1 (n) · · · yk (n) · · · yK (n) ∈ RK×1 .

(6)

and it can also be expressed as

As Figure 2 illustrates, the overall control signal vector is formed by stacking the above control signal fromn − L + 1 iteration to n iteration ashiTyk (n) = yk (n) yk (n − 1) · · · yk (n − L + 1) ∈ RL×1 ,(7)
iTh
Y(n) = yT1 (n) · · · yT k (n) · · · yT K (n) ∈ RKL×1 ,(8)

in which yk (n) stands for the k-th control signal to drive the corresponding secondary source. L means thelength of secondary path.
Subsequently, the anti-noise vector is obtained fromy′ (n) = S(n)Y(n) ∈ RM×1 ,where the secondary path matrix is expressed assT (n)
 11
 T
 s21 (n)S(n) = 
 ..
 .


sTM1 (n)···sT1K (n)

···
..
.



sT2K (n) 
M×KL.
..  ∈ R. TsMK (n)

···

(9)

(10)

In the above matrix, smk (n) represents the impulse response of the secondary path from the k-th secondary
source to the m-th error sensor:
h
iT
(2)
(L)
smk (n) = s(1)∈ RL×1 .
(11)
(n)
s
(n)
·
·
·
s
(n)
mk
mk
mk
According to above analysis of forward propagation, it is found that the control filter W(n) will contribute to
the anti-noises y′ (n), y′ (n + 1), · · · , and y′ (n + L − 1). Thus, updating W(n) requires future gradient knowledge,
which violates the causal restriction in real ANC systems.

Figure 3. The back propagation of the McFxLMS algorithm.
2.2 Back propagation
To tackle the causal problem during updating, we assumed that the adaptive filtering is a slowly changing
process, which means that
W(n) ≈ W(n − 1) ≈ · · · ≈ W(n − L + 1).
(12)
Therefore, the forward propagation of the McFxLMS algorithm can be modified as shown in Figure 3. The k-th
control signal is obtained fromJyk (n) = ∑ wTk j x j (n),j = 1, · · · , J and k = 1, · · · , K

(13)

j=1

and its vector format can be rewritten ashiTyk (n) = ∑Jj=1 wTk j x j (n) ∑Jj=1 wTk j x j (n − 1) · · · ∑Jj=1 wTk j x j (n − L + 1) ∈ RL×1 .

(14)

Hence, the m-th anti-noise can be calculated asKy′m (n) = ∑ ŝTmk yk (n)m = 1, · · · , M

(15)

k=1

where ŝmk denotes the estimate of the secondary path smk (n).
Moreover, the cost function of the McFxLMS algorithm is defined as the sum of squared error signal oneach error sensor:
M 
M
2
(16)
J = ∑ e2m = ∑ dm (n) − y′m (n)mmwhere dm (n) is the disturbance picked up by the m-th error sensor.
Through the above discussion, we can get the updating graph of the control filter wk j (n) as shown in Figure
4. According to back propagation mechanism and chain derivation rule, the gradient with respect to wk j can be

Figure 4. The computing graph of the control filter wk j (n) in the McFxLMS algorithm under the slow adapting
assumption, where j = 1, · · · , J and k = 1, · · · , M.
calculated by∂J∂ yk (n) M ∂ e2m (n) ∂ y′m (n)=∑ ∂ y′m (n) ∂ yk (n)∂ wk j∂ wk j m=1
hi M= − x j (n) · · · x j (n − L + 1) ∑ 2em (n)ŝmk∇wk j =

(17)

m=1

M

= −2 ∑ em (n)x′jkm (n),m=1where the filtered reference signal vector is given byhix′jkm (n) = x j (n) · · · x j (n − L + 1) ŝmk .

(18)

Finally, by using the negative value of the gradient (17) to update the control filer, we can get
wk j (n + 1) = wk j (n) −Mµ∇wk j = wk j (n) + µ ∑ em (n)x′jkm (n)2
m=1

k = 1, · · · , K and j = 1, · · · , J(19)where µ denotes the step size.
After the analysis of forward and back propagation, we found that the adaptive ANC algorithm may be
implemented via automatic derivation mechanism. Since the automatic derivation mechanism in PyTorch can
update weights given the cost function, the back propagation process can be automatically achieved without
resorting to extra-human efforts. Also, existing optimizers in PyTorch tool like SGD, Adam etc. can be directly
employed to update the control filters. Owing to the simple implementation method, changing the number ofmicrophones and loudspeakers in multiple-channel ANC systems is more convenient, so that the practicality
is enhanced. Additionally, based on the PyTorch tool, it is convenient to add constraints on the control filter
coefficients, such as L1 and L2 normalization.

3

SIMULATION RESULTS

We implemented the McFxLMS and McFxNLMS algorithm based on the automatic derivation mechanism in
PyTorch. In the ANC system, the number of reference sensors, secondary sources and error sensors are 4,

Figure 5. Error signals and averaged noise reduction level of every 1 second on the aircraft noise.

Figure 6. Error signals and averaged noise reduction level of every 1 second on the helicopter noise.

4, and 4, respectively. The control filter length is 512 taps. The step size of the McFxLMS algorithm andMcFxNLMS algorithm are set to 0.00001 and 0.001 separately. The primary path and secondary path arechosen as a band-pass filter and a low-pass filter.
The implemented McFxLMS algorithm and McFxNLMS algorithm are evaluated to suppress several realrecorded noises including: an aircraft noise with a frequency range of 50Hz-12, 000Hz, a helicopter noise witha frequency range of 50Hz-9, 800Hz, and a traffic noise with a frequency range of 40Hz-1, 400Hz. In thissection, the stochastic gradient descent (SGD) algorithm (18) was used for optimization.
The noise reduction results using the implemented McFxLMS algorithm and McFxNLMS algorithm on theaircraft noise, helicopter noise, and traffic noise are shown in Figure 5, Figure 6, and Figure 7. According
to the simulation results, the implemented McFxLMS and McFxNLMS algorithm can attenuate the real-world
noises, which demonstrates the effectiveness of the implementation method. Also, compared with the McFxLMS
algorithm, the McFxNLMS algorithm obtains slightly higher steady-state noise reduction levels on the aircraft
noise and helicopter noise. However, the McFxNLMS algorithm responds more slowly to the traffic noise thanthe McFxLMS algorithm.

Figure 7. Error signals and averaged noise reduction level of every 1 second on the traffic noise.

4

CONCLUSIONSIn this paper, we implement the McFxLMS and McFxNLMS algorithm based on the back propagation mechanism. Since the automatic derivation in PyTorch can update weights given the cost function, the back propagation of McFxLMS and McFxNLMS can be automatically achieved without resorting to extra-human efforts.
Therefore, the simple implementation method of the McFxLMS and McFxNLMS algorithm can improve thepracticality. Also, we provide the open source code of the implementation method. Simulation results show thatthe implemented McFxLMS and McFxNLMS algorithm are effective to attenuate different real noises. Furthermore, this method is expected to implement other adaptive algorithms in multi-channel ANC systems.

ACKNOWLEDGEMENTS
This research is supported by the Singapore Ministry of National Development and the National Research Foundation, Prime Minister’s Office under the Cities of Tomorrow (CoT) Research Programme (CoT Award No.
COT-V4-2019-1). Any opinions, findings, and conclusions or recommendations expressed in this material arethose of the author(s) and do not reflect the views of the Singapore Ministry of National Development andNational Research Foundation, Prime Minister’s Office, Singapore.

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[8] Kuo SM, Finn BM. A general multi-channel filtered LMS algorithm for 3-D active noise control systems.
Second Int Con on Recent Developments in Air and Structure Borne Sound and Vibration, Auburn AL.
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[9] Elliot S, Nelson P, Stothers I, Boucher C. In-flight experiments on the active control of propeller-induced
cabin noise. Journal of Sound and Vibration. 1990;140(2):219-38.
[10] Shi D, Gan WS, Lam B, Wen S. Feedforward selective fixed-filter active noise control: Algorithm andimplementation. IEEE/ACM Transactions on Audio, Speech, and Language Processing. 2020;28:1479-92.
[11] Garas J. Adaptive 3D sound systems. vol. 566. Springer Science & Business Media; 2012.
[12] Elliott S, Stothers I, Nelson P. A multiple error LMS algorithm and its application to the active control ofsound and vibration. IEEE Transactions on Acoustics, Speech, and Signal Processing. 1987;35(10):1423-34.
[13] Kinoshita S, Kajikawa Y. Multi-channel feedforward ANC system combined with noise source separation. In: 2015 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference(APSIPA). IEEE; 2015. p. 379-83.
[14] Shi D, Lam B, Ooi K, Shen X, Gan WS. Selective fixed-filter active noise control based on convolutional
neural network. Signal Processing. 2022;190:108317.
[15] Luo Z, Shi D, Gan WS. A Hybrid SFANC-FxNLMS Algorithm for Active Noise Control Based on Deep
Learning. IEEE Signal Processing Letters. 2022;29:1102-6.
[16] Shi D, Gan WS, Lam B, Wen S, Shen X. Active noise control based on the momentum multichannel
normalized filtered-x least mean square algorithm. In: INTER-NOISE and NOISE-CON Congress andConference Proceedings. vol. 261. Institute of Noise Control Engineering; 2020. p. 709-19.
[17] Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, et al. Pytorch: An imperative style, highperformance deep learning library. Advances in neural information processing systems. 2019;32.
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421-36.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0686

Practical Considerations In The Implementation Of Adaptive Filters
For Active Noise Control In The Earbuds
Agustinus OEY1
1

VizWave Inc., Korea

ABSTRACT
Active noise cancellation is becoming increasingly a common featured technology for in-ear personal audio
devices. With limited options on component allocation, power consumption, and manufacturing cost, theactive noise control algorithms used in the commercial products are generally based on the fixed-type
controller system. It has robust performance and simple structure, which is realizable with a low-cost digital
signal processor. The main drawback is the inability to compensate the change in the acoustic transfer paths,
for example, due to the variation in the earpiece fitting condition. Therefore, an alternative considered in thisarticle is the use of adaptive-type active noise control systems especially ones that employ adaptive filters.
To cope with the increase of system complexity, design concept and implementation strategy are discussed
in respect of actual hardware limitations. One realization of the filtered-x least mean square based active
noise control algorithm with a low-cost fixed-point digital signal processor in a commercial earbuds structure
is presented as case study.
Keywords: Active noise cancellation, Adaptive filter, DSP implementation

1. INTRODUCTION
Use of active noise control (ANC) method to reduce ambient noise in the earbuds is a commercial
success. It is a concrete example that demonstrates the effectiveness of the method in the frequency
range where the spatial control region is small in comparison to the wavelength. The problem itself
can be simply considered as cancellation between the plane waves. However, it comes with a set ofchallenges to be addressed because littleness is one of the key features to be presented in the earbuds.
Apart from the difficulty to fit all the required components into a tiny enclosure, tight spacing between
sensor and actuator limits the response time of an ANC system. This leads to the need for low latency
audio processing devices and computationally efficient control algorithms. A significant reduction ofnoise over an extended bandwidth can only be achieved by minimizing the latency (1).
Another important factor to be considered for a well performing ANC system i s the variation of
acoustic leakage in the acoustic control region. It is associated with user preference on diverse earbuds
fit conditions for a comfortable wear. In some occasion, the fit is also loosened when the user move.
Obviously, stronger anti-noise signal is required to compensate the increase in acoustic leakage. This
introduces uncertainty in way a controller would response. Consequently, controller stability and noise
reduction performance must be assured in the assumed perturbed range.
One earliest example of robust controller design for active headset is shown in (2). The two Riccati
equation algorithm is utilized for finding proper parameters of a controller with guaranteed operating
margins. An alternative approach is proposed in (3) that employs a group of stable feedback controllers
having various preset gains. In response to separate fit conditions, a comparator switches the operating
controller. These works provide an insight that a degree of adaptiveness is generally required to copewith the varying acoustic environments.
Adaptive controller with digital filter has been a popular choice for ANC applications. However,
it is somewhat demanding to be realized in the earbuds due to limitation in computational resources.
This article discusses the practical considerations to implement adaptive filter for noise cancellation
using a choice of digital signal processor (DSP) which is realistic to be put in the earbuds. Details on
1

oeyaugust@vizwave.net

the arrangement of speaker and microphones are in reference to one commercial earbuds product. To
operate the adaptive controller, the well-known filtered-x least mean square algorithm (FxLMS) is
incorporated. The overall specification is set based on computational resources and functional features
available in the selected DSP. Finally, experimentation with broadband random noise is presented.

2. Adaptive noise control system
Fig. 1(a) illustrates a simplified ANC system in the earbuds. For reducing ambient noise, which isassumed to be random and broadband, a feed-forward controller is typically adopted. It requires one
speaker to generate the anti-noise and two microphones, one positioned at the upstream and anotherone at the downstream, to measure the reference input, 𝑥(𝑡), and the noise residue, 𝑒(𝑡), respectively.
If the speaker and error microphone are put in a sealed enclosure, there are two propagation paths to
be considered. The first one is called the primary path, 𝑃(𝜔), by which the noise is travelled from thereference microphone to the error microphone. It is purely acoustical medium. The other one is called
the secondary path, 𝑆(𝜔), that stays between controller output and input ports. It is partially electricalmedium, that belongs to the circuitry in the signal interface unit, speaker, and error microphone, andacoustical medium in the space between speaker and error microphone.
The heart of the adaptive controller is a digital filter, which is generally classified into two majorclasses, i.e., recursive and non-recursive. The former reuses a part of its output as the input, creating
a feedback loop. In this work, the digital filter is non-recursive to ease convergence in the adaptation.
It is composed of one row of unit delays, where a segment of input data is stored, and another row ofcoefficient memories having the same length. The output of the digital filter is the sum product of thevalues in the two corresponding rows. Together with an algorithm for adjusting filter coefficients, anadaptive controller is constructed.
2.1 A review on FxLMS algorithm
In this work, the least mean square (LMS) algorithm is referred. The algorithm changes the filter
coefficients iteratively in the way that minimizes noise residue by taking the negative direction of theerror gradient. However, the existence of secondary path causes phase m ismatch on the arrival of theanti-noise and impedes the correct filter update. Therefore, an auxiliary filter must be inserted in thecontrol loop to compensate the alteration of anti-noise by the secondary path (4). The aforementioned
auxiliary filter is a secondary path estimate, 𝑆̂(𝑧), that can be obtained by transfer function modelingor by measurement. This approach is known as the FxLMS algorithm.
Fig. 1(b) shows a block diagram of an adaptive feed-forward controller, 𝑊(𝑧), embodied in a nonrecursive filter having a length of 𝐿. The output of the controller is the anti-noise signal, 𝑦(𝑛), thatcan be calculated using the following relation,𝐿𝑦(𝑛) = ∑ 𝑤𝑙 (𝑛)𝑥(𝑛 − 𝑙) = 𝑤 𝑇 (𝑛)𝑥(𝑛)
𝑙=0

(1)

Here, 𝑤𝑙 denotes the 𝑙-th coefficient of the controller. Then, the anti-noise signal is travelled throughthe speaker to produce,(2)𝑒(𝑛) = 𝑑(𝑛) + 𝑦 ′ (𝑛) = 𝑝𝑇 (𝑛)𝑥(𝑛) + 𝑠 𝑇 (𝑛)𝑦(𝑛)which is the noise residue measured by error microphone. The positive sign represents the sound wave
superposition between the noise and the anti-noise as it arrives at the control point.
The gradient of error surface can be obtained by differentiating cost function, 𝐽(𝑛) = 𝑒 2 (𝑛), withrespect to the filter coefficient. Applying the gradient descent algorithm, the iterative process to adjust
controller coefficients is expressed as follow,
𝑤(𝑛 + 1) = 𝑤(𝑛) − 𝜇 𝑥′(𝑛) 𝑒(𝑛)
(3)
′ (𝑛)
𝑇 (𝑛)
Here, 𝜇 denotes the iteration step that is associated with convergence speed and 𝑥
= 𝑠̂
𝑥(𝑛)
represents the filtered reference input. Iteration step is a positive coefficient that can be selected froma value smaller than,1
𝜇𝑚𝑎𝑥. =
(4)‖𝑥′(𝑛)‖2 (𝐿 + 𝛿𝑆 )Notations 𝜇𝑚𝑎𝑥. and 𝛿𝑆 represent the maximum applicable iteration step and the inherent delay in thesecondary path. Apparently, the delay in the secondary path is a constraint to convergence speed (5).
Longer path delay is translated into slower convergence.

(a)

(b)

𝑃(𝜔)
Ref. mic𝑥(𝑛)Speaker𝑑(𝑛)Err. mic

𝑒(𝑛)

𝑷(𝒛)
𝑦′(𝑛)

Noise

𝑺(𝒛)
𝑆(𝜔)
𝑾(𝒛)

Audio
input

𝑦(𝑛)

Signal interface circuits𝑥′(𝑛)Adaptive controller

෡(𝒛)
𝑺

LMS

Figure 1. (a) ANC system in the earbuds. (b) Components of an FxLMS based controller
2.2 The importance of secondary path
If a perfect noise cancellation is possible, that is 𝑒(𝑛) → 0 as the adaptation converges, the optimal
form of controller, 𝑊𝑜 (𝑧), can be derived from Eq. (1) and Eq. (2),𝑃(𝑧)𝑊𝑜 (𝑧) = −(5)𝑆(𝑧)For attenuating broadband random noise, the transfer function of the controller, 𝑊(𝑧), must represent
the impulse response of the optimal controller, which is realizable on the condition that the inverse of𝑆(𝑧) is existed. Therefore, having secondary path that can be represented with a causal and minimum
phase transfer function is desirable. In practice, the delay in the secondary path has to be smaller thanthe primary path. The optimal controller form also indicates that when a non-recursive filter is usedas the controller, it requires sufficient length to accommodate the rational part of the equation.
Fortunately, the associated control plant is expected to be of low order because the acoustical volume
in the earbuds is relatively small.
2.3 Practical considerations
Causality condition has to be satisfied by an ANC system to allow a broadband noise cancellation.
It is met when the time required for the anti-noise to be generated and delivered to the control pointis smaller than noise propagation time across the primary path. In short, causal condition is satisfied
when delay in the electrical path is smaller than the acoustical path. The main contributors of electricaldelay are time for signal conditioning, conversion, and computation. Signal conditioning in the antialiasing and reconstruction filters creates a latency that is proportional to filt er order and inversely
proportional to filter corner frequency. Time for signal conversion between analog and digital domains
is related to the type of the converter and the number of bits involved. For instance, given the same
resolution, Delta Sigma ADC is usually slower that SAR ADC. Computation in the controller occupies
one sample period in which the processor executes an adaptive control algorithm. Latency of speakerand microphones also contributes electrical delay.
Delay of acoustic primary path can be varied by a number of factors. In the earbuds, device fitting
and enclosure provide passive isolation that could increase delay in the primary path ( 6). On the other
hand, the acoustic leakage reduces the delay. Intuitively, the lowest estimate of acoustic delay, 𝛿𝑎𝑐𝑡 ,can be estimated from direct sound propagation,
𝛿𝑎𝑐𝑡 = (∆𝑥𝑟𝑒 − ∆𝑥𝑦𝑒 ) / 𝑐0(6)Here, ∆𝑥𝑟𝑒 and ∆𝑥𝑦𝑒 are the distance between the two microphones and the distance between speakerand error microphone, respectively, and 𝑐0 is the sound speed, which is about 343 m/s. However,when the route of the arriving noise is closer to the error microphone than the reference microphone,
the acoustic delay may not be sufficient to assure causality (7). This conditio n is purely physical andless related with the allocated filter length in the controller. The practical remedies are to increase
acoustic path delay by improving passive isolation and to use multi-reference method.

Coherence in the measurement defines the noise reduction performance of an ANC system. This isbecause adaptation of controller coefficients relies on two correlated information provided by error
microphone and reference microphone. Based on the analysis of random processes, the expected noise
reduction is given by,
2 (𝜔))
𝑁𝑅(𝜔) = 10 𝑙𝑜𝑔10 (1 − 𝛾𝑥𝑒
𝑑𝐵
(7)
2 (𝜔)
Where 𝛾𝑥𝑒
is the coherence function between the output of reference microphone and the output
of error microphone when the ANC system is inactive (8). This means coherence is more affected by
the quality of instrumentation such as microphone dynamic range, sensitivity, and directivity, as well
as distortion in the signal amplification unit. In addition, cable shielding and circuit isolation can help
to minimize input contamination from signal interference.
Besides its relation to the system latency, proper positioning of speaker and microphones is also
important in view of controllability. The obvious place for a speaker is in the enclosure of the earbuds.
However, the opening of ear tip can be extended beyond the ear canal open end. This opening creates
an impedance mismatch where sound waves are transmitted and reflected. Conceptually, the optimal
position of the speaker is at the dominant anti-node. In relation to the reference microphone, controller
complexity can be reduced if the microphone pick-up negligible amount of the anti-noise radiatedfrom the speaker. Therefore, it is desirable to block the acoustic feedback path by proper design ofthe enclosure. For error microphone, it is ideally located near the speaker, at the location where noise
residue is in presence with high correlation to the reference noise.

3. Implementation of adaptive ANC
High-performance DSP is needed in the controller development. There a number of commercial
DSPs which are designed for ANC applications. In this work, evaluation board EVAL-ADAU1787Z
from the Analog Devices is used. The board is shown in Fig. 2(a). It is equipped with four ADC
channels, two DAC channels, low-power audio codec, and two fixed-point DSP cores. The first coreis a programmable FastDSP audio processing engine that provides built-in biquad filters, signal
limiters, mixers, and volume controls. At sampling frequency of 768 kHz, a group delay of 5μs canbe expected when bypassing a signal from the ADC input to the DAC output (9). The length of the
program is limited to 64 instructions. The second one is a 28-bit SigmaDSP audio processing core
which offers additional built-in functions, including FIR filters and custom algorithms. Depending on
the given sampling frequency, the acceptable program length can vary from 32 instructions at 768 kHz
to 512 instructions at 48 kHz. The core also supports high-performance mode by using overclock that
doubles the number of instructions.
Comprehensive design of earbuds can make significant impact on noise cancellation performance.
Low-latency electroacoustic components are essential to be used in the system. How these components
are arranged in a well-shaped geometry of the enclosure defines interaction between the noise and theanti-noise. There are many aspects to be considered in developing a well performing noise cancelling
earbuds; however, this work rather emphasizes on the realization of the adaptive controller. Therefore,
the earbuds used in the experimentation is taken from the Bose QC30. Roughly, it has a dimension of
28 x 30 x 20 mm. Two 4 mm electret microphones and one 15 mm speaker with an impedance of 32Ω
can be found in the enclosure, which are connected to the main board in the neckband using cables.
The distance between two microphones is about 8.5 mm and the distance between speaker and error
microphone is about 2 mm. Therefore, the acoustic delay in the arrangement is about 19μs.
The operating bandwidth of the controller can be defined from the earbuds passive noise isolation.
A measurement was conducted in a listening booth using an artificial head and torso (HEAD Acoustic
HTB V) and a loud-speaker as the sound source. The speaker was positioned in front of the ear at a
distance of 1 m. A broadband, uniformly distributed random noise was used as the excitation signal.
By comparing the internal microphone responses when the earbuds were and were not attached to theears, the passive noise isolation plot shown in Fig. 2(b) can be obtained. If a significant noise reduction
is anticipated to be at least 10 dB, the operating bandwidth would be up to 1 kHz.
3.1 Software development tool
Analog Devices provides a graphical programming environment for writing and deploying signal
processing program on the evaluation board. The software is composed of two basic frameworks; thefirst one provides access at the DSP register level for assigning built -in operational features, such as
power management, conditioning filters, interpolator and decimator channels, and for managing signal

(b)Noise attenuation

end
(a)

5
-5
-15
-25
0

500
1000
1500
Frequency (Hz)2000

Figure 2. (a) DSP evaluation board and the earbuds. (b) Earbuds passive noise isolation.
routings between input and output (I/O) ports and the DSP cores. The second framework is schematic
tools where a collection of functional blocks can be put together to perform signal manipulation andcontrol. The composed schematic sets device working flow that is called repeatedly at the beginningof a sampling period. Each schematic block costs computation resources in terms of instruction cycle
and memory. Since the system supports less instruction at high sampling frequency, it is important toonly use computationally efficient block. The memory is relatively plentiful.
There are cases when schematic block essential to ANC application could not be utilized because
it requires too many instruction cycles. For example, a built-in L-tap FIR filter spends 13 instruction
cycles for the function overhead and L+8 instruction cycles for the sub-routines overhead. Besides
that, the coefficients of the filter are not feasible to be accessed and modified during the execution.
Therefore, for implementing an efficient ANC program, it is necessary to use supplementary programthat gives access to low level functionality such as shift register, multiply and accumulate (MAC),
and memory read/write. An L-tap FIR filtering can be carried out with L cycles of MAC instruction
and 1 cycle of memory transfer. The shifting of filter data is automatical ly done in the shift registerat the start of a sampling period. Details of low-level programming are not discussed in this article.
3.2 Design of the controller
To gain an initial information about the acoustic path in the earbuds. A measurement was conductedin using the aforesaid test equipment. The excitation signal is a sine-swept. In the measurement of the
primary path, the signal is sent to an external loud-speaker. Impulse response function between thetwo microphones is measured. For measuring secondary path, the signal is sent to earbuds speaker.
The path response is measured from DSP output port which has a bypass connection to earbuds error
microphone. The result taken from the measurement at the sampling frequency of 96 kHz is presented
in Fig. 3(a). Apparently, the primary path impulse response function has lower peak amplitude than
the secondary path due to higher path attenuation. One would notice the first peak in the primary path
impulse response comes after the secondary path, which is an indication of system causality.
The algorithm for the adaptive controller is implemented in the SigmaDSP core that supports accessto custom program. To result a causal ANC system, the delay in the electrical path has to be smaller
than the acoustical path, which is about 19 μS. The feasible choice of the sampling frequency is started
from 96 kHz that corresponds to 256 instruction cycles in the normal clock mode. About 43 instruction
cycles are reserved for core housekeeping. Therefore, the whole algorithm, inc luding the assignmentof the I/O ports, must be fitted into a total of 213 instruction cycles.
The basic block of FxLMS algorithm requires three I/O ports, one filter as the controller, one filter
to model secondary path estimate, and one functional block for coefficient adaptation. The breakdownof instruction allocations is disclosed in Tab. 1. Recalling to Fig. 3(a), the required length when a nonrecursive filter is used to represent secondary path estimate can be considerably long, about 100 taps
to cover every microsecond. Therefore, it is beneficial to utilized a stable recursive filter to model thesecondary path estimate. The optimal length of the recursive filter was calculated using the line searchmethod, which are 16 for the feed-forward filter and 19 for the feedback filter. Fig. 3(b) compares theimpulse response functions of the measured and the modeled secondary paths.
An impulse response function of optimal controller estimate is shown in Fig. 4(a). It is calculated
without regularization from the measured acoustic paths. Although is not accurate, the estimate helps

0.2

0.2

Impulse response(b) 0.3

Impulse responseend.
(a) 0.3
0.1
0

-0.1
-0.2

0.1
0
-0.1
-0.2

-0.3

-0.3
0

1

2

3

4

0

1

2

Time (μS)

34Time (μS)

0.1
0.05

(b) 25
Noise reduction (dB)(a)
Impulse response

Figure 3. (a) The measured impulse response functions of the earbuds primary path (red) andsecondary path (blue). (b) Comparison between impulse response functions of themeasured (blue) and the modeled (red, dashed) secondary paths.

0
-0.05

20
15
10

-0.1

5
0

0

1

2

3

4

5

0

200

400

600

800

1000

Frequency range (Hz)Time (μS)

Figure 4. (a) A non-regularized impulse response function of the optimal controller estimate.
(b) Controller noise reduction: 𝑁𝑑 = 𝑛 (green), 𝑁𝑑 = 2𝑛 (red), 𝑁𝑑 = 4𝑛 (blue)
Table 1 – Basic computation requirements for various programming schemes
Computation process

Computation cost (instruction cycle)
FxLMS (1)FxLMS (2)FuLMS (3)Core housekeeping
ADC: Reference signal
ADC: Error signal
DAC: Control signal

43

43

43

2

2

2

2

2

2

2

2

2

Controller output
Filtering of input
Filtering of output
Controller adaptation

𝐿𝑊 + 1

𝐿𝑊 + 1(𝐿𝑊𝐵 + 𝐿𝑊𝐴 ) + 1

𝑆𝑊 + 1(𝑆𝑊𝐵 + 𝑆𝑊𝐴 ) + 1(𝑆𝑊𝐵 + 𝑆𝑊𝐴 ) + 1--(𝑆𝑊𝐵 + 𝑆𝑊𝐴 ) + 1

2 + 3𝐿𝑊

2 + 3𝐿𝑊

4 + 3(𝐿𝑊𝐵 + 𝐿𝑊𝐴 )Notes(1). 𝑊(𝑧) and 𝑆̂(𝑧) are non(1). recursive(2). 𝑊(𝑧) is non recursive,(2). 𝑆̂(𝑧) is recursive(3). 𝑊(𝑧) and 𝑆̂(𝑧) are(3). recursive
Notation B and A indicate
the order is associated to
the feed-forward and thefeedback part, respectively

to provide an initial guess for the required length in the controller filter. Looking from the estimate,
the first one microsecond of the impulse response function carries more than 90% of the signal power.
The length of the controller could be set in the vicinity of 100 to resemble dominant optimal response,
however, it is not realistic for the given computation constraints. Alternatively, a recursive filter canbe used as the controller, however, as summarized in Tab. 1, additional instructions must be allocatedfor output filtering in the adaptation of feedback filter. In addition, controller stability can be at risk
during the adaptation. Therefore, a method based on the multi-rate signal processing is applied (10).
The length of the filter in the controller is set to 40-tap that corresponds to a total of 248 instruction
cycles. A few more were allocated for a second order recursive filter, which is inserted somewhere at
the upstream. The filters for signal conditioning were set in the DSP register window.
Controller performance for cancelling broadband random noise at different multi-rate factor, 𝑁𝑑 ,is shown in Fig. 4(b). The slopes are varying around 450 Hz. When a small multi-rate factor is given,
the observation time becomes short that makes hard for the controller to regulate the low frequency
components; vice versa. When 𝑁𝑑 is set to 2𝑛, an average noise reduction higher than 10 dB was
achieved in the range up to 1 kHz. Further improvement can be expected by setting SigmaDSP in thehigh-performance mode; assuming additional filter taps are allocated in the controller. Biquad filtersin the FDSP core can also be utilized for modeling of multiple secondary path estimates.

4. CONCLUSIONS
A study on the implementation of adaptive controller using a low-cost fixed-point DSP for noise
cancelling earbuds has been presented. Maintaining a low latency system is the key for causality andassuring controller performance. Learning from the case, the limitation in the computational resources
is a relevant issue to be addressed in the use adaptive filter. Nevertheless, signal processing techniques
provide practical solution for achieving the desired noise reduction.

ACKNOWLEDGEMENTS
The author would like to thank Dr. Ji-Ho Chang (Korea Research Institute of Standards and Science,
Daejeon) and Prof. Sung-Hwan Shin (Kookmin University, Seoul) for granting access to test facility
and experimentation devices.

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1. Liebich S, Fabry J, Jax P, Vary P. Signal processing challenges for active noise cancellation headphones.
Speech Communication; 13th ITG-Symposium; 2018. pp. 1-5.
2. Bai MS, Lee DJ. Implementation of an active headset by using the H∞ robust control theory. J Acoust
Soc Am. 1997;102(4):2184-2190.
3. Goldstein AL. Adaptive feedback control for earbuds headphones and handset. Patent Application
Publication; 2016; US 2016/0300562 A1.
4. Morgan DR. An analysis of multiple correlation cancellation loops with a filter in the auxiliary path. IEEE
Trans. Acous. Speech Sig. Proc. 1980;Vol. ASSP-28(4):454-467.
5. Kuo SM, Morgan DR. Review of DSP algorithms for active noise control. Proc. IEEE Int. Conf. Contr.
App.; 25-27 September 2000; Anchorage, USA. p. 243-248.
6. Zhong X, Zhang D. Latency prediction of earmuff using a lumped parameter model. Applied Acoustics
2021;176.
7. Zhang LM, Qiu ZJ. Causality study on a feedforward active noise control headset with different noise
coming directions in free field. Applied Acoustics 2014;80:36-44.
8. Hansen CH, Snyder S, Qiu XJ, Brooks L, Moreau D. Active Control of Noise and Vibration. Second
Edition, CRC Press; 2012. p. 380-382.
9. Analog Devices. Four ADC, two DAC, low power codec with audio DSPs ADAU1787. Analog Device
Datasheet, 2020.
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Int. 2009;48:567–573.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0077

Development of active equalization control system for in-ear
headphones
Chong-Rui Huang1; Cheng-Yuan Chang1; Sen M. Kuo1
1

Department of Electrical Engineering, Chung Yuan Christian University, Taiwan

ABSTRACTThe current headphones do not allow consumers to enable hear-through (HT) with active noise control (ANC)
function, which leads to the noise disturbing the ambient sound. This research developed an active
equalization control (AEC) system that integrates ANC with HT techniques to reduce the ambient noise while
listening to the ambient sound of interest. The proposed AEC system uses a novel filtering structure to provide
diverse listening experiences for consumers, which improves the quality of communication in noisy
environments and allows consumers to adjust the performance level and bandwidth according to preferences.
Finally, the effectiveness of the proposed system is verified by using objective measurements of spectral
differences.
Keywords: Active noise control, Hear-through, Headphones

1. INTRODUCTION
With the rapid growth of the hearables market, active noise control (ANC) and hear-through (HT)technologies have become indispensable standard features in today's headphones [ 1]. While ANC
eliminates the main noise based on the principle of superposition [2], HT compensates for the acoustic
attenuation of the headphones via external ambient sound [3].
To effectively reduce ambient noise, these headphones usually use ANC to supplement the pas sive
isolation of the headphones to fully isolate external ambient noise and ensure a quieter listening
experience [4]. However, this also makes it difficult to listen to external ambient sounds, such as
conversations, security announcements, ambient sounds of interest, etc. Therefore, the HT function
provides consumers with a natural listening experience as if there were no headphones. The main
sources of ambient noise come from traffic noise, such as low frequency noise from cars, planes, ortrains [5]. However, when we talk to each other in a noisy traffic environment, although theheadphones already provide consumers with ANC and HT modes, one limitation of the current
headphones is that it does not allow consumers to turn on ANC and HT modes at the same time.
Therefore, while listening to the external ambient sound, there will still be noisy low frequency noise,
which leads to the degradation of conversation quality. In recent years, the concept of active
equalization control (AEC) has been applied to headphones and hearing aids to help define therequired magnitude response [6-7] and provide consumers with a variety of listening needs, such as
reduced occlusion effect [8], enhance acoustic transparency [9], adaptive equalization [10], and so on.
Based on the AEC concept, this paper designed the control filter for ANC and the equalization
filter for HT using the adaptive filtering algorithm, and this was then combined with the proposed
selective filtering structure to allow consumers to individually adjust the gain and bandwidth of ANC
and HT systems, providing consumers with a diverse listening experience and to reduce the ambient
noise while listening to the ambient sound of interest. Finally, we validate the proposed system using
objective measurements of spectral differences in simulation. The rest of this paper is organized asfollows. Section 2 defines the operating frequency range of ANC and HT systems based on the ambient
noise, passive isolation of the in-ear headphones, and the hearing area of the human ear. Section 3
proposed the AEC system, with an overview of both the ANC and the HT filter design method. Section
4 verified the proposed control system and discussed the performance of ANC, HT, and ANC+HT
modes by spectral. Section 5 draws conclusions.
1

rayhuang@cycu.org.tw, ccy@cycu.edu.tw, kuo1065@gmail.com

2. Measurement analysis
This study defines the operating frequency range of ANC and HT systems based on the frequency
spectrum of ambient noise, passive noise isolation of the headphones, and the hearing area of thehuman ear in order to reduce the ambient noise while listening to the ambient sound of interest, andthen to improve the quality of speech. The most prominent source of ambient noise is traffic noise [5].
In accordance with previous noise measurement methods [11], it was determined that the noise energy
generated by buses, airplanes, and Taiwan High Speed Rail is mainly distributed at low frequencies
below 500 Hz, as shown in Figure 1. Various types of headphones have different passive isolation.
The passive isolation of over-ear headphones and in-ear headphones can generally attenuate the noisefrom 500 Hz but fails to effectively attenuate the low-frequency noise below 500Hz [12]. Figure 2
presents the passive isolation of the in-ear headphone adopted in this study, which revealed that thepassive isolation performance of the in-ear headphone was determined by the DOA of the ambient
sound [13]. In Figure 9, with a primary loudspeaker placed 30 cm from the right ear of the KEMAR,
pink noise was played as the ambient noise, and a 360-degree rotating disc (with a total of 8 angles,of which each is at 45° apart) under the KEMAR was used to evaluate the DOA of passive isolationof the in-ear headphone. In Figure 2 shows that blue block was derived by deducting the KEMAR
measurement without in-ear headphone from the KEMAR measurement with in-ear headphone at eachangle and then applying the median measurement for each angle to determine the blue line. Under
such circumstances, the magnitude attenuations of ambient sound below 4 kHz are nearly equi valent,but after 4 kHz, if a fixed equalization filter is used, HT system is prone to changes in the performanceof the HT system due to magnitude deviations. The results of past experiments [14] support this point
very well. With the explanation above, the main processing range of ANC system is defined below
500 Hz (red area) to cancel low-frequency ambient noise, while the main processing range of the HT
system is 500 Hz to 4 kHz (green area) to compensate for passive isolation of in-ear headphone.

Figure 1 – The spectrum of traffic noises.

Figure 2 – Passive isolation of in-ear headphone.

Figure 3 – The schematized presentation of the average speech spectrum [16].
The hearing area of the human ear shows that a person with normal hearing can perceive sounds
in the range of 20 Hz~20 kHz, and the speech range starts at around 100 Hz and ends at around 7 kHz[15], and the main consonant area of human speech is illustrated by the average speech spectrum inthe range of 250 Hz to 4 kHz [16-17], as shown in Figure 3. Therefore, in order to improve theconversation quality in the noisy environment and to avoid the speech loss caused by the ANC system,the ANC system only needs to handle the ambient noise below 250 Hz in the ANC+HT m ode. In
addition, consumers are allowed to adjust the performance level and operating frequency range of the
ANC and HT systems according to their personal preferences, where the performance level can becontrolled by adjusting the gain and the operating frequency range can be controlled by switching theshaping filter. The control method of the system will be explained in detail in Section 3.3.

3. Proposed system
This section presents the design method of active equalization control (AEC) system which
includes three modes (ANC, HT, and ANC+HT). The HT mode can perfectly restore the environment
sound at the eardrum of a wearer of in-ear headphones; The ANC mode can effectively cancel theenvironment noise at the eardrum of a wearer of in-ear headphones; ANC+HT mode combines ANC
and HT capabilities to improve call quality in noisy environments for a wearer of in -ear headphones.
Figure 4 presents the concept of the AEC system presented in this paper and illustrate the relevanttransfer functions of in-ear headphone in digital models, in which the KEMAR acts as a measurement
standard. The primary pathdenotes the relative transfer function with in-ear headphone between
the external microphone to the internal microphone. Instead of identifying the primary path, thisstudy used the primary loudspeaker to generate pink noise as ambient noise, an external microphone
is attached to the outside of the in-ear headphone to receive external ambient sound, and theresidual ambient sound in the KEMAR ear (an internal microphone) is denoted as. The target
path
denotes the relative transfer function without in-ear headphone between the external
microphone to the internal microphone. The secondary pathdenotes the transfer function fromthe secondary speaker to the internal microphone, which includes the digital to analog converter(DAC), reconstruction filter, power amplifier, the acoustic path from the secondary speaker to theinternal microphone, pre-amplifier, anti-aliasing filter, and analog to digital converter (ADC). In
addition, the most significant element is the acoustic path from the secondary speaker to the internal
microphone. The secondary path model
can be estimated by offline modeling method [2], whichis required by the filtered-X LMS (FXLMS) algorithm to compensate for the effects of secondary path.
is the feedback path transfer function from the output of the AEC system. This study does
not consider
because the silicone tip of in-ear headphone is enough to avoid sound leakage ofin-ear headphone. We used the primary loudspeaker to generate white noise as excitation signals to
identify theandtransfer functions. Finally, this study identifies the transfer functions,, andto provide FXLMS algorithm [2] training control and equalization filters.

Figure 4 – The transfer functions of in-ear headphone.
3.1 Control Filter Design
The goal of the ANC mode of the AEC system is to cancel the residual ambient noise
According to Figure 4, the optimal control filterin the steady state is defined as.

(1)However, optimal control filter
is usually not achievable. Because the secondary path
includes the acoustic path delay from the secondary speaker to the internal microphone and may havenon-minimum-phase characteristics [18]. Therefore, it is impossible to compensate for the inherent
delay caused by
if the primary pathdoes not contain a delay of at least equal length [2].
The causality constraint needs to be satisfied in the broadband feedforward control system; otherwise,
the performance of the ANC system to cancel random broadband noise will be degraded [ 19].
Especially in the small size of in-ear headphones, the cause causality constraint is more important. A
higher sampling rate is usually used to reduce hardware latency to satisfy causality. Thus, the higher
sampling rate requires a larger filter length to must have sufficient resolution in time to model therequired response[2]. Figure 5 presents a block diagram of the ANC system using the
FXLMS algorithm [2] for deriving the control filter W(z), where the update algorithm can be
expressed as(2)w(n) converges to the optimal value with a sufficiently small step. Finally, this study used
as a control filterof length
to verify the performance of ANC system.
3.2 Equalization filter Design
The goal of the HT mode of the AEC system is to compensate for the passive isolation of theheadphones to reproduce the ambient sound. We assume the residual ambient soundfor simplicity. According to Figure 4, optimal equalization filterin steady state is defined as(3)
The practical equalization filter
must compensate for the inherent delay caused by thesecondary pathin order for the feedforward adaptive filter to converge and achieve a flat
magnitude response [8]. Therefore, thedelayed samples are included to overcome eliminate thecausality constraint of the broadband feedforward control system is expressed as(4)
where determinedfrom the impulse response of the secondary path
to be a delay of 7
samples. Figure 6 presents a block diagram of the HT system using the FXLMS algorithm [3] for
deriving the equalization filter, where the update algorithm can be expressed as(5)
Theconverges to the optimal value with a sufficiently small step. Finally, this study used
as an equalization filterof length
to verify the performance of the HT
system. Based on the passive isolation of the headphones measured in Section 2, we defined the HT
system to compensate only in the 500 Hz to 4 kHz range. Therefore, a band -pass shaping filter
with cutoff frequencies of
500 Hz and
4 kHz is used to avoid excessive amplification ofambient noise above 4 kHz due to DOA.

Figure 5 – Block diagram of ANC system using

Figure 6 – Block diagram of HT system using thethe FXLMS algorithm.

FXLMS algorithm.

3.3 Active Equalization Control System
The proposed AEC system uses a novel feedforward filtering structure, which contains a control
filter, an equalization filter, selective shaping filter, and two manual gains
andas shown in Figure 7. The AEC system can be switched to ANC, HT, and ANC+HT modes bychanging the filters,, and, as shown in Table 1. In addition, the manual gains
andare used to adjust the performance levels in ANC and HT modes. The filter
is used tolimit the compensation range of the HT system, and filter
is used to control the frequency
range of noise cancellation in ANC+HT mode. The following equation describes the effect of thesefilters on the behavior of the AEC system.
(6)

Figure 7 – Block diagram of the active equalization control (AEC) system.
Table 1 – Switching modes between ANC, HT, and ANC+HT in AEC system.
AEC System

Operating Modes
ANC

HT

ANC+HT

N/A
Filter & Gain

N/A
N/A

Figure 8a presents the final design of the overall transfer functions of the in -ear headphone system,
including the primary path, the target path model, the secondary path model, the control Filter, the equalization filter
and the shaping filtersand.
For the ANC mode, Figure 8a and Figure 8b show that magnitude and phase response of the red(denote) and gray (denote) lines are very similar below 500 Hz, which indicates thatthe designed control filter. This means that the ANC system can effectively cancel
external ambient noise
below 500 Hz. For the HT mode, Figure 8a shows that the magnitude
response of the orange (denote) and green (denote) lines are very similar in therange of 500Hz to 4kHz, which indicates that the designed equalization filter.
This means that the HT system can effectively compensate for the passive isolation of the headphones,
allowing external ambient sound below 4 kHz to pass through the headphones naturally, that is,

. For the ANC+HT mode, The AEC system combines the capabilities of ANC and HT, inwhich the shaping filter
is used to limit the HT system to compensate only at 250 Hz~4 kHz.
Equation 6 describes the behavioral impact of the ANC system with the HT system. This allows the
HT system (denote) to compensate for passive isolation in the 250 to 4 kHz range
while using the ANC system (denote) to cancel the residual ambient noise
below 250
Hz to improve conversation quality in environments with low-frequency noise.

(a)

(b)

Figure 8 –The transfer functions of the AEC system: (a) Magnitude response and (b) Phase response.

4. Evaluate
4.1 Measurement Setup
The measurements were conducted in an anechoic chamber in the Active Noise and Vibration
Control Applications Development Center (ANVC), CYCU, complying with ASTM E336 (2009) andISO 3745 (2003) standards, as shown in Figure 9a. We recorded the sounds using an audio interface
device (Mytek Digital, Brooklyn ADC) and then performed simulations to verify the effectiveness ofthe proposed system. A primary loudspeaker (Tang Band, W8-1808) was placed 30 cm away from the
KEMAR right ear (GRAS, KB5000 Right Anthropometric Pinna) to generate excitation signals. We
placed a rotating disk under the KEMAR to evaluate different DOA sounds to analyze passive isolationof in-ear headphone, where KEMAR contains 8 azimuths from 0⁰ to 315⁰ in 45⁰ steps, as Figure 9b.

R

(a)

L

(b)

Figure 9 – (a) Experimental setup; (b) The setup to test different DOA.
To the outer shell of an in-ear headphone (Sennheiser IE 40 Pro) was attached one MEMS microphone(Knowles, SPU0414HR5H-SB) as an external microphone and used KEMAR's right ear as an internal
microphone, where signals are connected to DSK6713 (Texas Instruments, TMS320C6713 DSP
Starter Kit) with an interface card (HEG Co., Ltd., DSK6713IF -B). The sampling frequencyisset 48 kHz, and the cutoff frequencyof low pass filters (Reconstruction and anti-aliasing filter)
was 20 kHz. Also, the secondary pathconsiders the latency effects of acoustic and electronic
paths.
4.2 Objective verification
In this section, the simulations are used to demonstrate the ability of the proposed AEC algorithm
to an in-ear headphone. This study aims to demonstrate that the AEC system can effectively achieve
ANC and HT capability and demonstrate the benefits provided by the ANC+HT mode in a noisy
environment. The parameter values used for this simulation are listed in Table 2. We assumed theestimated secondary path model
perfectly model the secondary path
. Furthermore, thereference signal
and the ambient sounds
andare obtained in the experimental
environment of KEMAR at 270° position to provide simulation validation and to ensure theeffectiveness of the proposed system. Figure 10 shows the simulation results for all modes (ANC, HT,
and ANC+HT) of the AEC system, and it is clearly visible that the ANC mode (red line) can effectively
attenuation the low-frequency component below 500 Hz, and HT mode (green line) can effectively
compensate for the high-frequency component below 4 kHz. Finally, the proposed ANC+HT mode
(pink line) can not only attenuate the low-frequency component below 250 Hz but also compensate
for the passive isolation of headphone from 250 Hz to 4 kHz. Figure 11a and Figure 11b show the
manual gain
andto the performance level of the ANC and HT system. Furthermore, Figure
11c shows that the filter
can effectively control the frequency range of noise cancellation in
ANC+HT mode by adjusting the cutoff frequency(e.g.,
3300, 600, or 1000). This study
validates the simulation results of the proposed AEC system by subjective analysis. It proves that the
AEC system can provide consumers with a diverse listening experience.
Table 2 – Parameter setting
Sampling frequency

and Cutoff frequency

48 kHz, 20 kHz

Length of FIR filter secondary path model

200

Length of FIR target path model

300

Length of FIR control filter

3000

Length of FIR equalization filter

150

Samples of delay

7

Filter order of IIR shaping filter

5

Cutoff frequency of IIR shaping filter: 500Hz,: 4 kHz

Filter order of IIR shaping filter

7

Cutoff frequency of IIR shaping filter: 300, 600, 1000 Hz;: 4 kHz

Figure 10 – Simulation results of the AEC system including ANC, HT, and ANC+HT for three operating
modes according to Table 1.

(a)

(b)

(c)

Figure 11 – Influence of the gains and shaping filters on the AEC system: (a) manual gain
manual gain

, and (c) shaping filter

.

, (b)

5. CONCLUSIONSThis study develops an AEC system for in-ear headphone, which offers consumers a diverse
listening experience, improves the quality of hear-through in noisy environments, and extends thelimits of current headphones. The proposed selective filter structure is validated by simulation, which
can efficiently switch between ANC, HT, and ANC+HT modes and selectively adjust the gain andbandwidth of ANC and HT. Finally, the validity of the proposed system is verified by using objective
measurements of spectral differences. In the future, we will study the speech enhancement systemapplied to the AEC system to improve speech quality in a noisy environment. We will also use real time experiments to validate the AEC system and subjective assessments by the listening test.

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ABS-0179

Kernel-interpolation-based spatial active noise control
with exterior radiation suppression
Kazuyuki ARIKAWA, Shoichi KOYAMA, and Hiroshi SARUWATARI(1)(1) Graduate School of Information Science and Technology, The University of Tokyo, Japan, ak1217@g.ecc.u-tokyo.ac.jp

ABSTRACTA spatial active noise control (ANC) method based on kernel interpolation of a sound field with exterior radiation
suppression is proposed. The aim of spatial ANC is to reduce incoming noise over a target region by using
multiple secondary sources and microphones. The method based on kernel interpolation of a sound field allows
noise attenuation in a regional space with an array of arbitrary geometry. The cost function is defined as theacoustic potential energy, i.e., the regional integral of the power distribution inside the target region. However,this cost function does not take into consideration the exterior radiation of secondary sources. Thus, the acoustic
power in the exterior region can be amplified by the output of the secondary sources. We propose two spatial
ANC methods with exterior radiation suppression. The first approach is based on the minimization of the costfunction formulated as a sum of the interior acoustic potential energy and exterior radiation power. The second
approach is based on the minimization of the interior acoustic potential energy with inequality constraints on
the exterior radiation power. Adaptive algorithms for minimizing the cost function are derived for the two
approaches. Numerical experimental results indicate that the proposed methods can reduce the interior regional
noise while suppressing the exterior radiation.

Keywords: Active noise control, Kernel interpolation, Exterior radiation, Adaptive filtering

1

INTRODUCTION

Active noise control (ANC) is aimed at canceling incoming primary noise by emitting anti noise signals fromsecondary sources [5, 8, 11]. Multichannel ANC algorithms are typically applied to attenuate the primary noise
at multiple control points by minimizing the power of the signals observed at error microphones. However,this conventional ANC takes only discrete positions into consideration; therefore, there is no guarantee that the
primary noise is reduced in the region between the positions.
Sound field recording and reproduction techniques [7, 12, 18, 20, 22] have led to the recent developmentof spatial ANC methods aimed at attenuating noise in a continuous target region [1, 3, 6, 9, 19, 23]. In
particular, spatial ANC methods based on the kernel interpolation of the sound field [3, 4] have the advantages
that arbitrary configuration is allowed for the microphone array placement and there is no need for the prior
identification stage required in virtual sensing techniques [10].
Meanwhile, if we consider applications such as noise reduction inside automobile cabins [15], it is desirable
to suppress the exterior radiation from the secondary sources to a certain level so that the secondary sources do
not produce large noise outside the target region. The cost function used in the previous kernel-interpolationbased ANC method is the acoustic potential energy inside the target region; therefore, the previous method
does not take into consideration the exterior radiation. Although ANC methods with a constraint on the output
power of secondary sources have been investigated [13, 14, 16, 17], restricting the output power of secondary
sources does not necessarily lead to the suppression of exterior radiation in the spatial ANC. We propose ANC
methods to suppress exterior radiation from secondary sources while reducing noise inside the target region. We
consider two approaches: the first approach is to add a penalty term corresponding to exterior radiation power
to the cost function used in the previous study, i.e., the acoustic potential energy inside the target region, andthe second approach is to put inequality constraints on the external radiation power and minimize the same

Reference microphone

Error microphone: Target region

Primary noise

Secondary source

Figure 1. Arrangement of spatial ANC system.
cost function as in the previous method. We formulate normalized least-mean-square (NLMS) algorithms in thefrequency domain to adaptively update the control filter for both approaches. Numerical experiments show thatthe proposed methods can reduce noise inside the target region while maintaining less exterior radiation than in
the previous kernel-interpolation-based method.

2

SPATIAL ACTIVE NOISE CONTROL BASED ON KERNEL INTERPOLATIONLet Ω ⊂ D be a target region where D = R2 or R3 and M error microphones are placed in Ω. L secondary
sources and R reference microphones are placed outside Ω, as shown in Fig. 1.
The driving signals of the secondary sources and the observed signals of the reference and error microphones
at angular frequency ω are denoted as y (ω) ∈ CL , x (ω) ∈ CR , and e (ω) ∈ CM , respectively. Hereafter, weomit the argument ω for notational simplicity. The goal of spatial ANC is to reduce primary noise in Ω byappropriately setting the driving signals y based on the observed signals x and e . When denoting the primarynoise at the error microphone positions as d ∈ CM , the error microphone signals are represented as
e = d + Gy,(1)

where G ∈ CM×L consists of the transfer functions from the secondary sources to the error microphones, which
we assume to be given in advance. The driving signals are calculated as
y = W x,(2)where W ∈ CL×R is the control filter matrix, which is adaptively updated to minimize a certain cost function
J.
In spatial ANC based on kernel interpolation [3], the cost function is defined as the acoustic potential energy
in the interior region of Ω as
Jint :=

Z|ûe (rr )|2 drr ,(3)Ω

where ûe (rr ) is the pressure field inside Ω estimated by kernel ridge regression. By using the estimation formulaof ûe (rr ) described in [3], Jint can be represented as
Jint = e H A int e ,(4)where A int is the Hermitian matrix defined as
Aint := PHZΩκ ∗ (rr )κ
κ T (rr ) drr P.

(5)

K +λ I M )−1 , where K ∈ CM×M and κ (rr ) ∈ CM are the Gram
Here, (·)H denotes the complex conjugate and P = (Kmatrix and the vector consisting of the kernel function κ(·, ·), respectively. The kernel function is defined as(
J0 (k∥rr − r ′ ∥2 ) if D = R2′,
(6)
κ(rr , r ) :=j0 (k∥rr − r ′ ∥2 ) if D = R3
where k denotes the wave number, ∥ · ∥2 denotes the ℓ2 -norm, and J0 (·) and j0 (·) are the 0th-order Bessel andspherical Bessel functions of the first kind, respectively. The NLMS algorithm for updating W to minimize
Jint is derived as∂
Jint
W ∗ W =W∂W
Wnµ0
G H A int e n x H=Wn−n,GH A int G ∥2 ∥xxn ∥22 + ε∥G

W n+1 = W n − µn(7)where µ0 ∈ (0, 2) is the normalized step-size parameter, and ε > 0 is a regularization parameter to avoid zero
division. x n and e n are the observed signals at the nth iteration.

3

SPATIAL ACTIVE NOISE CONTROL WITH EXTERIOR RADIATION SUPPRESSION

Noise reduction inside the target region is achieved by minimizing Jint in (4), but it can possibly lead to unacceptably large exterior radiation power from the secondary sources. Now, we formulate two adaptive filtering
algorithms to suppress exterior radiation power while reducing noise in the target region. The representationof exterior radiation power from the secondary sources is introduced in Section 3.1, and the NLMS algorithms
with a penalty term or inequality constraints are derived in Sections 3.2 and 3.3, respectively.
3.1 Derivation of exterior acoustic radiation
Let ΩS be a circular or spherical area including Ω and all the secondary sources. The total acoustic powerradiated by the secondary sources, or the exterior radiation power, is defined as [21]


Z
1
j ∂
Re us (rr )us (rr )∗ drr ,(8)
Jext :=
ρck ∂ n∂ ΩS 2where ρ is the density of the air, c is the sound speed, Re[·] denotes the real part of the complex number,us (rr ) is the pressure field produced by the secondary sources, and ∂ /∂ n denotes the normal derivative. By
representing us (rr ) with the driving signals y , Jext can be expressed as [21]Jext = y H A ext y .

(9)Here, A ext is the Hermitian matrix determined by the positions and directivity patterns of the secondary sources.
When all the secondary sources are point sources, each element of A ext can be represented as1J0 (k∥rr l − r l ′ ∥2 ) if D = R28ρck
Aext )ll ′ =
(A
,
(10)
1


j0 (k∥rr l − r l ′ ∥2 ) if D = R38ρck
where r l is the position of the lth secondary source. The general representation for arbitrary directivity patterns
is also shown in [21].

3.2 NLMS algorithm with penalty term
To minimize sound pressure inside Ω with suppression of the external radiation from the secondary sources, wedefine a new cost function Jpenal as
Jpenal := Jint + λ Jext ,(11)

where λ > 0 is the regularization parameter for the penalty term in kg/s. By substituting Jpenal instead of Jintin the derivation of Eq. (7), the NLMS algorithm with a penalty term for exterior radiation is derived as
W n+1 = W n − µn (GGH Aint en + λ Aext yn )xxH
n.

(12)

Here, µn is the step size at the nth iteration and is defined as
µn =

µ0
,
GH A int G + λ A ext ∥2 ∥xxn ∥22 + β
∥G

(13)

where µ0 and β are the same parameters as in Eq. (7).
3.3 NLMS algorithm with inequality constraints
The difficulty with the NLMS algorithm with a penalty term is the necessity of an appropriate setting of theregularization parameter λ . If λ is large, sound pressure inside Ω will not be sufficiently reduced. In contrast,
if λ is small, the external radiation power can be too large. Another difficulty is that the external radiation canbecome large during the adaptation process even if the external radiation after the convergence of the control
filter is acceptable.
To overcome the above difficulties, we reformulate the spatial ANC problem as an optimization problem
with inequality constraints as
minimizeW)
Jint (Wsubject toW ) ≤ C.
Jext (WW ∈CL×R(14)

We here explicitly represent Jint and Jext as functions of the control filter W . C > 0 is the maximum acoustic
power radiated by the secondary sources. The optimization problem in Eq. (14) is equivalent to the minimization
problem of the cost function Jconst , which is defined as
W ) := Jint (WW ) + 1{WW ).
Jconst (WW ∈CL×R |Jext (WW )≤C} (W(15)

W ) ≤ C and ∞ otherwise. Both terms in the right
Here, 1(·) is the indicator function, which returns 0 if Jext (Wside of Eq. (15) are convex and Jint is differentiable with respect to W ; therefore, we can apply the proximal
gradient method [2] to minimize Jconst . The update rules, which we call the NLMS algorithm with inequality
constraints for external radiation, are represented as(n) −1
A−1
GH A int e n x H
Z n+1 = W n − µA
ext (Gn ) R xxỹyn+1 = Z n+1 x n
W n+1 = min 1, q

(16)
(17)

√
C
yn+1
ỹyH
n+1 A ext ỹ Z n+1 ,(18)

where µ in Eq. (16) is the step size determined as
µ=

µ0
.
−1 H
Aext G A int G ∥2 + β
∥A

(19)

2.0
1.5
1.0

Secondary source
Error microphone
Primary noise source

y (m)

0.5
0.0

−0.5
−1.0
−1.5
−2.0
−4

−3

−2

−1
x (m)

0

1

2

Figure 2. Experimental setup.
(n)Here, µ0 and β are the parameters defined in the same way as in Eqs. (7) and (13). R xx is the estimation of R xx
at the nth iteration, where R xx := E x x H is the autocorrelation matrix of the reference microphone signals. If(n) −1(n) −1(n)
the number of reference microphones R = 1, R xx
can be estimated as 1/∥xxn ∥22 . If R ≥ 2, Λ xx:= R xxis estimated as−1
R(n−1)Λ (n)+ (1 − α)xxn x Hxxxx = (αR
n)
"
#
(n−1)
(n−1)
Λxx
Λxx
1
x n )Hx n )(Λ
(Λ
(n−1)
Λxx −
=
.
(n−1)
α
xH
xn + αn Λ xx(20)1−αHere, α ∈ (0, 1) and we apply the Sherman-Morrison formula to derive Eq. (20). Furthermore, to avoid theinstability of calculating the inverse of A ext , we replace A ext in Eqs. (16) and (19) with A ext + ηII L (η > 0) if
the condition number of A ext in the ℓ2 -norm is larger than a certain threshold.

4

EXPERIMENTS

4.1 Settings
We conducted numerical experiments to evaluate the proposed methods. We assumed a two-dimensional freefield in the experiments. The target region Ω was a circular region with a radius of 0.5 m, whose center was set
at the coordinate origin, as shown in Fig. 2. The numbers of secondary sources and error microphones were set
to L = 12 and M = 24, respectively. Secondary sources were placed at regular intervals on circles with radii of
0.9 m and 1.1 m, and error microphones were placed on circles with radii of 0.47 m and 0.53 m. A single source
was placed as the primary noise source at (−3.0 m, 0.2 m), and the reference microphone signal was directly
obtained from the noise source. All secondary sources and the primary noise source were point sources. The
noise signal is constant in the frequency domain, and Gaussian noise was added to the error microphone andreference microphone signals at each iteration so that the signal-to-noise ratio became 40 dB.
As an evaluation measure of ANC, we define the regional noise power reduction inside Ω as(n)

Pred (n) := 10 log10(n)∑ j |ue (rr j )|2(n)∑ j |up (rr j )|2

(n)

,

(21)

where r j is the jth evaluation point in Ω, and ue and up represent the total pressure field and primary noise
field at the nth iteration, respectively. We set 1240 evaluation points at regular intervals inside Ω. The externalradiation power from secondary sources was calculated using Eq. (9).

−12.50.0175−13.0

0.0150−13.5

0.0125−14.0

Pred (dB)ext (kg m2/s3)

0.0200−14.5

0.01000.0075−15.0

0.0050−15.5

0.0025

−16.0
0.0

0.2

0.4

λ

0.6

0.8

1.0

(a) External radiation power. Red line indicates(1/2)Jˆext .

0.0

0.2

0.4

λ

0.6

0.8

1.0

(b) Regional noise power reduction

Figure 3. External radiation power and regional noise power reduction of Ext-Penal NLMS for each regularization parameter at 600 Hz.
We compared the NLMS algorithm with the penalty term for external radiation (Ext-Penal NLMS), the
NLMS algorithm with inequality constraints for external radiation (Ext-Const NLMS), and the NLMS algorithm
without exterior radiation suppression (NLMS). Aint was computed using Eq. (5) with numerical integration, andA ext was computed using Eq. (10). The sound speed c and the air density ρ were set to 340 m/s and 1.3 kg/m3 ,respectively. We replaced A ext with A ext +ηII L in Ext-Const NLMS when the condition number of A ext exceeded
102 , where η was set to 10−5 . The parameters µ0 and β in Eqs. (7), (13), and (19) were set to 0.9 and 10−8 ,respectively.
We denoted the external radiation power produced when the secondary sources were driven with the Wiener
filter of NLMS, i.e., the convergence point of Eq. (7), as Jˆext . The maximum radiation power C used in ExtConst NLMS was set to (1/2)Jˆext . We determined the regularization parameter λ used in Ext-Penal NLMS
by exhaustive search. Figures 3a and 3b show the change of external radiation power and regional noise power
reduction at 600 Hz when λ was varied from 0 to 1.0. Figure 3a indicates that λ should be set larger than
0.1 kg/s to suppress the radiation power to less than (1/2)Jˆext . On the other hand, Fig. 3b shows that thenoise reduction performance monotonically decreases as λ increases. In the experiments, we set λ as 0.1 at
600 Hz so that the external radiation power after convergence became close to (1/2)Jˆext . We note that theabove procedure to select the parameter λ is infeasible in practice since the Wiener filter cannot be computedin advance.
4.2 Results
Figure 4a shows the noise reduction performance at each iteration when the noise frequency was 600 Hz. The
final noise reduction performance was almost the same among the three methods, whereas the convergence of
Ext-Const NLMS was slower than those of the other methods. This slow convergence is due to the smaller
step size than in the other methods. Figure 4b shows the external radiation power at each iteration. The final
radiation powers for Ext-Penal NLMS and Ext-Const NLMS were half of that for NLMS, as expected. In
Fig. 5a, Pred after 5000 iterations are plotted with respect to the frequency from 100 to 1000 Hz at intervals of
10 Hz. The parameter λ for Ext-Penal NLMS was selected at each frequency in the same way as described in
Section 4.1. It can be seen that the noise reduction performance was almost the same among the methods at
most frequencies. Figure 5b shows Jext after 50000 iterations. Jext for Ext-Const NLMS was smaller thanthat for Ext-Penal NLMS below 420 Hz. It can be considered that the final output power of the secondary
sources became smaller on replacing A ext with A ext + ηII L in Ext-Const NLMS at frequencies below 420 Hz.
We also investigated the performance of the methods when the primary noise source moved during the adaptation process. The position of the primary noise source was (−3.0 m, 0.2 m) for the first 25000 iterations, andNLMS
Ext-Penal NLMS
Ext-Const NLMS

−6−80.02000.01750.0150ext (kg m2/s3)

0.0125Pred (dB)−100.0100−12

0.00750.0050−140.0025−16

NLMS
Ext-Penal NLMS
Ext-Const NLMS

0.0000
0

10000

20000
30000
Number of iteration

40000

0

50000

(a) Regional noise power reduction

10000

20000
30000
Number of iterations

40000

50000

(b) Exterior radiation power

Figure 4. Regional noise power reduction and exterior radiation power at each iteration when noise frequency
was 600 Hz.

−10

0.030

NLMS
Ext-Penal NLMS
Ext-Const NLMS

NLMS
Ext-Penal NLMS
Ext-Const NLMS

0.025

−15

−30

Pred (dB)

−25

ext

0.020

(kg m2/s3)

−20

0.015
0.010

−35

0.005

−40
200

400
600
Frequency (Hz)800(a) Regional noise power reduction

1000

0.000

200

400
600
Frequency (Hz)

800

1000

(b) Exterior radiation power

Figure 5. Regional noise power reduction and exterior radiation power after 50000 iterations with respect tofrequency.
(−2.0 m, 0.2 m) for the next 25000 iterations. All the parameters were set the same as those described in Section 4.1. Figure 6a shows Pred at each iteration when the frequency was 600 Hz. Although Pred instantaneously
increased when the position of the primary noise source changed at n = 25000, the three methods successfully
tracked the change of the noise source position. Figure 6b shows Jext at each iteration. For NLMS and ExtPenal NLMS, Jext became larger after the primary noise source moved, whereas Jext remained the same for
Ext-Const NLMS. The final exterior radiation powers for NLMS and Ext-Penal NLMS depend on the primarynoise source signals, which are difficult to estimate. In contrast, we can expect the same exterior radiation
power for Ext-Const NLMS irrespective of the primary noise source signals, since the acceptable maximum
external radiation power is determined in advance.

5

CONCLUSION

We proposed spatial ANC methods with the suppression of exterior radiation from secondary sources. We
considered two cases: the addition of a penalty term corresponding to the exterior radiation power to the original
cost function and the reformulation of the optimization problem with inequality constraints with respect to theexternal radiation power. The NLMS algorithms to update the control filter were derived for both cases. The

2.5

NLMS
Ext-Penal NLMS
Ext-Const NLMS

0.0

0.025
ext (kg m2/s3)−2.5
Pred (dB)

NLMS
Ext-Penal NLMS
Ext-Const NLMS

0.030

0.020

−5.0
−7.5

0.015

−10.0

0.010

−12.5

0.005

−15.0

0.000
0

10000

20000
30000
Number of iteration

40000(a) Regional noise power reduction

50000

0

10000

20000
30000
Number of iterations

40000

50000

(b) External radiation power

Figure 6. Regional noise power reduction and exterior radiation power at each iteration when noise frequency
was 600 Hz and the position of the primary noise source changed at 25000 iterations.
NLMS algorithm with the penalty term converges faster than the NLMS algorithm with inequality constraints,
whereas the latter method has the advantage that the maximum acceptable external radiation power can be
set irrespective of the primary noise source signals. The results of numerical experiments indicated that the
proposed methods can reduce noise inside the target region while maintaining less exterior radiation than theprevious method.

ACKNOWLEDGEMENTS
This work was supported by JST FOREST Program (Grant Number JPMJFR216M, Japan).

References[1] B. Bu, C. Bao, and M. Jia. Design of a planar first-order loudspeaker array for global active noise control.
IEEE/ACM Trans. Audio, Speech, Lang. Process., 26(11):2240–2250, 2018.
[2] P. L. Combettes and V. R. Wajs. Signal recovery by proximal forward-backward splitting. Multiscale
Model. Simul., 4(4):1168–1200, 2005.
[3] H. Ito, S. Koyama, N. Ueno, and H. Saruwatari. Feedforward spatial active noise control based on kernelinterpolation of sound field. In Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), pages 511–
515, Brighton, May 2019.
[4] H. Ito, S. Koyama, N. Ueno, and H. Saruwatari. Spatial active noise control based on kernel interpolation
with directional weighting. In Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), pages 8399–
8403, May 2020.
[5] Y. Kajikawa, W. S. Gan, and S. M. Kuo. Recent advances on active noise control: open issues andinnovative applications. APSIPA Trans. Signal Inf. Process., 1, 2012.
[6] S. Koyama, J. Brunnström, H. Ito, N. Ueno, and H. Saruwatari. Spatial active noise control based onkernel interpolation of sound field. IEEE/ACM Trans. Audio, Speech, Lang. Process., 29:3052–3063, 2021.
[7] S. Koyama, K. Furuya, Y. Hiwasaki, and Y. Haneda. Analytical approach to wave field reconstruction
filtering in spatio-temporal frequency domain. IEEE Trans. Audio, Speech, Lang. Process., 21(4):685–696,
2013.
[8] S. M. Kuo and D. R. Morgan. Active noise control: a tutorial review. Proc. IEEE, 87(6):943–973, 1999.

[9] Y. Maeno, Y. Mitsufuji, P. N. Samarasinghe, N. Murata, and T. D. Abhayapala. Spherical-harmonic-domain
feedforward active noise control using sparse decomposition of reference signals from distributed sensor
arrays. IEEE/ACM Trans. Audio, Speech, Lang. Process., 28:656–670, 2019.
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[11] P. A. Nelson and S. J. Elliott. Active control of sound. Academic Press, 1991.
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PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0566

Active control of self-excited judder in a dry dual-clutchtransmission
Jihea Lim1; Seokhoon Ryu2; Young-Sup Lee3; Jangwon Lee4; Chang Kook Chae5
1-3

Department of Embedded Systems Engineering, Incheon National University, Korea
4, 5

Research & Development Division, Hyundai Motor Company, Korea

ABSTRACTA new active judder control algorithm to suppress self-excited judder in the driveline by applying active
damping through the use of a clutch actuator is proposed. Judder, which is torsional vibration of the drivelinethat may occur when the clutch disk is engaged with the engine flywheel, has been required to be improved
since it causes some negative effects such as wear of the clutch disk and passenger discomfort. Such judder
can be reduced by adding the anti-judder torque to the launch torque for transmitting driving power. The
suggested algorithm generates the anti-judder torque by adjusting the amplitude and phase of the juddersignal extracted from the input shaft speed. The proposed algorithm was implemented in an actual car having
a dry dual-clutch transmission and the real-time control experiments were carried out when the experiment
car was launched from a standstill on a flat paved road. The control experiment results showed that thesuggested algorithm can suppress the judder amplitude greatly.
Keywords: Active damping, Active judder control, Self-excited judder

1. INTRODUCTION
Clutch judder is an undesired longitudinal oscillation that is caused by the torsional vibration of
the driveline of a vehicle and occurs while the clutch disk is being engaged with the engine flywheel.
Especially, self-excited judder is due to the negative gradient of the friction coefficient of the clutch
disk [1].
Such judder leads to passenger discomfort, wear of the clutch disk, and also affects the driveabilityof the vehicle negatively. In order to suppress judder, active control methods have been c onsideredalong with passive control methods [2-5].
This study proposes a new active judder control (AJC) approach based on adaptive signal
processing methods to generate anti-judder torque for suppressing self-excited judder. An AJC system
was implemented in an actual car with a dry dual-clutch transmission (DCT), and the clutch actuator
was used to generate active damping as a secondary actuator.

2. Active judder control algorithm
The input and output of the AJC algorithm are the DCT input shaft speed and the anti-judder torque,
respectively. The self-excited judder e(n) is almost a sine wave whose amplitude is varying, and thus
the anti-judder torque is developed as follows.
Firstly, e(n) is extracted from the measured DCT input shaft speed using a peak filter, and thenit is decomposed into the estimate of the amplitude of the judder waveform signal Eˆ (n) and thenormalized judder waveform signal sin( (n)) . In this step, Eˆ (n) can be obtained by using the control

jhl@inu.ac.kr
yuzeng@ inu.ac.kr
3
ysl@ inu.ac.kr
4jangwonlee@hyundai.com
1
2

5

filter w(n) based on the least mean square (LMS) algorithm whose update equation is given by [6]w (n + 1) = w (n) −  ( e(n) + w T (n)x(n) ) x(n)(1)

where  is the convergence coefficient, and x(n) is the sine wave vector whose frequency is equal to thatof the judder signal. If w(n) is sufficiently converged by Equation (1), Eˆ (n) can be given asw T (n)w(n) . Next, the normalized judder waveform signal sin( (n)) is rectified to shape it to the form of

a positive half-wave. Finally, Eˆ (n) and the rectified sin( (n)) are multiplied and adjusted by a scaling
factor and a time-delay factor to generate anti-judder torque.

3. Experimental Set-up
The AJC system with the proposed algorithm was implemented in a car having a dry DCT for the
real-time control experiment. The control algorithm was embedded in a control unit (DS1041,
dSPACE) and operated at the sampling frequency of 400 Hz. The DCT input shaft speed which is the
input signal of the proposed algorithm was received from the TCU (transmission control unit), andthe anti-judder torque which is the output of the algorithm was transmitted to the TCU, and thenpassed on to the clutch actuator by being added to the launch torque for initiating the car.

4. Results and discussions
The test car at the first gear was creepily launched for about 5 seconds from a standstill on a flat
paved road and then was braked for about 2 seconds by force.

(a)(b)
Figure 1. Measured engine and input shaft speeds. (a) before control. (b) after control.
Figure 1(a) shows the measured engine and input shaft speeds before control. The self -excited
judder mainly occurred while the input shaft speed increased ranging from 400 to 800 RPM, and its
maximum amplitude of about 50 RPM at 2.6 sec after creep launch. As shown in Figure 1(b) whichdisplays the results after control, it was found that the judder was suppressed by the anti-judder torque.
In particular, the maximum judder amplitude after control was achieved to about 30 RPM which was
20 RPM lower than that before control.

5. Conclusions
In this study, a novel AJC algorithm to suppress self-excited judder included in the DCT input shaft
was investigated. The AJC algorithm generates the anti-judder torque from the judder signal byadjusting its amplitude and phase. The judder signal was extracted from the input shaft speed.
An AJC system based on the proposed algorithm was implemented in an actual car with a dry DCT,
and the real-time control experiment was carried out while the test car was creepily launched from astandstill. From the experimental result, the maximum amplitude of the judder was reduced from about
50 RPM before control to about 20 RPM after control by the active damping generated by the antijudder torque. This indicates that the suggested algorithm can suppress the judder amplitude.

REFERENCES
1. Mohire S, Kapse R, Tendulkar V. Study of Clutch Judder Phenomenon in Manual Transmission Vehicle
and Its Analysis Approach. SAE Technical Paper; 2019. No. 2019-26-0215
2. Klaus Küpper, Boris Serebrennikov, Georg Göppert. Software for automized transmissions –Intelligent
driving, LuK SYMPOSIUM 2006; 2006.
3. Kim J. An Automotive Clutch Control for Vibration Suppression of Dual Clutch Transmissions. SAE
Technical Paper; 2019. No. 2016-01-1114.
4. Bruce M, Egardt B, Pettersson S. On powertrain oscillation damping using feedforward and LQ feedback
control. Proceedings of the IEEE Conference on Control Application; 2005. p. 147-156.
5. Berriri M, Chevrel P, Lefebvre D. Active damping of automotive powertrain oscillations by a partial
torque compensator. Control Engineering Practice; 2008. 16(7):874-883.
6. Elliott S. Signal processing for active control. Academic Press, New York, USA; 2001.

ABS-0679

On the latency of voice conversion in an active voice cloning device
Obed IRIHOSE(1) , Rong XIE(2) , Chuang SHI(3)(1) University of Electronic Science and Technology of China, China, obed@std.uestc.edu.cn(2) University of Electronic Science and Technology of China, China, xierong@std.uestc.edu.cn(3) University of Electronic Science and Technology of China, China, shichuang@uestc.edu.cn

ABSTRACT
Although significant progress has been made in voice conversion (VC), the presence of the source speaker’s
original voice becomes problematic, especially in a real-time voice cloning scenario where listeners are close to
the source speaker. An overlapping of the source speaker’s voice and the converted voice results in a degradationof the sense of immersion to the converted voice. In this paper, we conceptualize an active voice cloning (AVC)
device, which can convert one’s voice timbre to another’s while confining the source speaker’s voice with active
noise control (ANC). The VC system is realized through a low-latency deep neural network model, and the
ANC system is constructed by a feedforward single-channel implementation. The mockup of the AVC device
is assembled in a short open tube that can be worn on the source speaker’s mouth. Taking into considerationthat the latency in the VC system introduces a phase difference between the converted voice and the residual
voice of the source speaker, we further assess its effect on the intelligibility of the converted voice, as well as
the overall performance of the AVC device in ameliorating the perceptual experience.

Keywords: Active voice cloning device, Voice conversion, Active noise control, Latency

1

INTRODUCTION

Voice conversion (VC) refers to the process of changing one person’s voice to sound like that of another person
while keeping the linguistic contents unchanged (1). VC has become an attractive topic in recent years as
it promises potential applications in different areas, such as speaker’s identity protection (2), singing voice
conversion (3), speech-aid for vocally impaired people (4), and virtual reality (5). VC can be classified into two
types: parallel VC and non-parallel VC. In parallel VC, parallel speech corpora of source and target speakers
are needed to perform a spectrum mapping, while in non-parallel VC, as its name infers, the training can bedone using unaligned corpora. From a practical point of view, the scarcity of parallel corpora needed brings
parallel VC a huge challenge. Thus, many works have placed emphasis on non-parallel VC as it does nothave the constraints posed by the need for parallel utterances and can benefit from a large scale of non-parallel
speech corpora.
Traditional VC methods have been studied based on the Gaussian mixture model (GMM), vector quantification, and dynamic time wrapping, but the advent of deep neural network (DNN) propels the advancementof VC. DNN models, such as variational auto-encoders (VAE) (6) and generative adversarial networks (GAN)(7), outperform traditional methods in improving the quality of the converted voice. However, DNN models arecomputationally expensive, and thus the quest for a low-latency VC has been subject to different studies in thepast years. For example, Ronssin and Cernak proposed an “almost causal” VC system, of which the look-ahead
was only 57.5 ms (8). Saeki et al. proposed a direct wave modification method combining a DNN model andthe short-tap sub-band filtering. It was reported that the look-ahead was also a few tens of milliseconds but theconversion time of a 25 ms waveform was only 5 ms (9).
Even though VC has achieved state-of-the-art results in both quality of the converted voice and low latency,
there is a remaining issue that must be addressed when applying VC in real-time voice cloning scenarios. The
presence of the source speaker’s voice results in a degradation of the sense of immersion to the converted

Source Speaker

Voice Converter

Converted
Voice

ANC Controller

Residual
Voice

Figure 1. System overview.
8cm

10cm
3cm

8cm

3cm

p

(a)

f

8cm

r

Mouth Simulator

Acoustic Setup of AVC Device

1

s

2

(b)

Figure 2. Mockup of AVC device: (a) photo; (b) cross-sectional design.
voice. When listeners are close to the source speaker, they can still hear both the source speaker’s voice andthe converted voice. Arakawa et al. proposed the use of a cone-shaped mask with sound-proof material inside
to confine the original voice from being leaked into the outside environment (10). Although this method wasable to reduce the source speaker’s volume to a certain extent, the closed design of the mask blocks the passageof air, making it uncomfortable for people to talk.
Inspired by the voice shutter (11), we conceptualize an active voice cloning (AVC) device able to convert
one’s voice timbre to another’s while confining the source speaker’s voice with active noise control (ANC). The
ANC technique transmits an anti-noise wave that has the same amplitude and opposite phase as the unwanted
noise wave. The anti-noise wave interferes with the noise wave, resulting in a reduced sound pressure levelbased on the principle of acoustic wave superposition (12, 13). In the AVC device, the source speaker’s voice
is treated as the noise wave. The advantage of using ANC in the AVC device is that the structure of the device
can be open, allowing a smooth mouth movement as well as a smooth passage of air.
Albeit, the AVC device faces two main challenges. Firstly, the VC conversion latency introduces a phasedifference between the converted voice and the residual voice of the source speaker. Secondly, the mutual
influence of VC and ANC causes degradation in suppressing the source speaker’s voice and deterioration in
the quality of the converted voice. Therefore, this paper describes our current mockup of the AVC device
and assesses the effect of the latency on the performance of the AVC device based on results of Mel cepstral
distortion (MCD) and a DNN-based mean opinion score evaluation method, namely MOSNet.

2

AVC DEVICEAs depicted in Figure 1, the AVC device consists of a microphone, a voice convertor, an ANC controller anda loudspeaker. The microphone is used to collect the source speaker’s voice. The voice converter converts thesource speaker’s voice into the target speaker’s. The ANC controller is used to generate the anti-noise wave tosuppress the source speaker’s voice. Lastly, the loudspeaker is used to play back the anti-noise wave and theconverted voice at the same time.

+

p

∑
+

f
+ ANC Controller

x

+

r

∑

-

fŝ

𝑥’

yc

w

+

∑

s

+
ŝ

e

LMS

yt

Voice Converter
Mel
Spectrogram
Extractor

CycleVAE

MWDLP

Figure 3. Schematic diagram of the AVC device.

Encoder

Decoder𝝓𝑥’

Mel Spectrogram
Extractor

MWLDP

yt

Excitation
Encoder

Decoder𝝓Speaker-code

Figure 4. Block diagram of the voice converter, which is extracted and modified from (14).
The mockup of the AVC device is shown in Figure 2. A mouth simulator is used to simulate the source
speaker for the voice converter and the primary noise source for the ANC controller. The microphone and theloudspeaker in Figure 2 are enclosed in a short open tube. The microphone also serves the purpose of thereference microphone for the ANC controller. A temporary error microphone is placed beside the AVC device,providing the error signal for the ANC controller and the voice that listeners hear for further assessment.
The block diagram of the AVC device is shown in Figure 3. There are four acoustic paths, which arealso indicated in Figure 2(b). They are the primary path p, the reference path r, the feedback path f, and thesecondary path s. The models of the feedback path and the secondary path are denoted as f̂ and ŝ, respectively.
The control filter w is trained by the filtered reference least mean squares (FxLMS) algorithm with feedback
path neutralization when the voice converter is not turned on. The primary noise is an equalized Gaussian
noise for it to have the same spectral envelope as that of the source speaker’s voice. After the error signal e
converges, the adaptation is terminated. The fixed control filter is then used with the voice converter.
Taking the conversion latency into consideration, we adopt the VC model proposed by Tobing and Toda in(14) to realize the real-time low-latency voice converter. The block diagram of the voice converter is depicted
in Figure 4. This voice converter consists of two encoders, i.e. φ and φ̃ , and two decoders, i.e. θ andθ̃ . The encoders and decoders form a cyclic VAE. The encoders take the Mel spectrogram of the source
speaker’s voice and encodes it to speaker independent features z and z̃. To reconstruct the Mel spectrogram ofthe source speaker’s voice from θ , z is blended with a time-invariant speaker-code and the excitation features

(a)

(b)

(c)

(d)

Figure 5. Acoustic path measured in the mockup of the AVC device mockup: (a) p; (b) r; (c) f; and (d) s.

Figure 6. Convergence curves for different source speakers.
that are estimated by θ̃ with z̃ and the same speaker-code. The Mel spectrogram is then recovered back toa waveform by a vocoder, namely the multiband WaveRNN with data-driven linear prediction (MWDLP) (15).
Fine-tuning is jointly carried out between the cyclic VAE and the MWDLP after the intermediate excitation
features are omitted. During the VC, the target speaker-code is used to generate the Mel spectrogram with thetarget speaker’s features. The generated Mel spectrogram is finally fed into MWDLP to synthesize a waveformof the target speaker’s voice.

3

SIMULATION RESULTS

Simulations were carried out with measured acoustic paths shown in Figure 5. The sampling rate was set to 24
kHz. The models of the secondary path and the feedback path were assumed to be perfect, i.e. ŝ=s and f̂=f.
The control filter had a length of 400 taps. The voice converter was trained based on the dataset provided by
the voice conversion challenge (VCC) 2020 (16). Source speakers’ utterances were filtered by the reference pathin advance. There were four source speakers in the dataset. 60 utterances from each speaker were used in the
training process, and 25 were used in the performance assessment of the AVC device. The voice converter had
an inherent latency of 27 ms. Extra latencies were artificially added in to assess the impact of the latency on
the performance of the AVC device. The sound pressure level (SPL) of the source speaker’s voice was assumed
to be 65 dB at the loudspeaker of the mouth simulator, while the target speaker’s voice was assumed to achieve
80 dB at the loudspeaker of the AVC device.
The convergency curves in the process of obtaining the control filter are shown in Figure 6. The results
are averaged across different utterances of each speaker. The noise reduction levels achieve 12.5 dB, 11.9 dB,

(a)

(b)

(c)

(d)

Figure 7. Effectiveness of the ANC controller on suppressing the source speaker’s voice: (a) Source speaker 1;(b) Source speaker 2; (c) Source speaker 3; and (d) Source speaker 4.

(a)

(b)

Figure 8. (a) MCD and (b) MOS of the converted voice with respect to the VC latency.
13.5 dB, and 13.7 dB for the four source speakers. Furthermore, Figure 7 demonstrates the waveforms at thetemporary error microphone when the ANC controller is turned on and off.
Mel cepstral distortion (MCD) and mean opinion score (MOS) are employed to evaluate the performance of
the AVC device. MCD is the spectral distance between the converted voice and its ground-truth voice. Lower
MCD indicates better VC performance (17). MOS is objectively calculated based on the pre-trained MOSNet(18), which is a deep-learning-based non-intrusive MOS predictor and reported to have a highly correlated
prediction to the subjective score. A higher MOS indicates better quality of a speech signal. Figure 8 shows
the MCD and MOS with respect to the VC latency in the AVC device. The trend of MCD indicates that a
VC latency around 100 ms should be avoided in the AVC device. Meanwhile, the trend of MOS suggests thatthe latency should be as low as possible to ensure better perceptual quality of the converted voice. With ANC
being incorporated into the AVC device, the MCD is reduced by 0.2055 and the MOS is improved by 0.0231
on average. This is due to the effective suppression of the source speaker’s voice by ANC.

4

CONCLUSIONSIn this work, an AVC device is conceptualized and the effect of the VC latency on the quality of the converted
voice has been assessed. The AVC device aims to convert one’s voice to sound like another’s while confining
the source speaker’s voice with ANC. This would be particularly useful in the real-time voice cloning scenario
where listeners are close to the source speaker. Once the source speaker’s voice can be suppressed, the senseof immersion to the converted voice is enhanced. Based on acoustic paths measured in a mockup of the
AVC device, simulations have been carried out. The simulation results demonstrate that the ANC controller
in the AVC device effectively suppresses the source speaker’s voice and improves the perceptual quality of
the converted voice regardless of the latency. Nevertheless, the perceptual quality of the converted voice issignificantly better when the VC latency is much lower than 100 ms.

ACKNOWLEDGEMENTS
This manuscript is prepared based on the research work supported by the National Natural Science Foundationof China and the Civil Aviation Administration of China (Joint Grant No. U1933127).

REFERENCES[1] Sisman, B.; Yamagishi, J.; King, S.; Li, H. An overview of voice conversion and its challenges: Fromstatistical modeling to deep learning. IEEE/ACM Transactions on Audio, Speech, and Language Processing,29, 2021, 132-157.
[2] Srivastava, B. M. L.; Vauquier, N.; Sahidullah, M.; Bellet, A.; Tommasi, M.; Vincent, E. Evaluating voice
conversion-based privacy protection against informed attackers. Proceedings of the 2020 International Conference on Acoustic, Speech, and Signal Processing (ICASSP), Barcelona, Spain, 2020, 2802-2806.
[3] Kobayashi, K.; Toda, T.; Nakamura, S. Intra-gender statistical singing voice conversion with direct waveform
modification using log-spectral differential. Speech Communication, 99, 2018, 211-220.
[4] Nakamura, K.; Toda, T.; Saruwatari, H.; Shikano, K. Speaking-aid systems using GMM-based voice conversion for electrolaryngeal speech. Speech Communication, 54 (1), 2012, 134-146.
[5] Sato, K.; Rekimoto, J. Voice conversion system based on deep neural network capable of parallel computation. Proceedings of the 25th IEEE Conference on Virtual Reality and 3D User Interfaces, Reutlingen,Germany, 2018, 677-678.
[6] Hsu, C. C.; Hwang, H. T.; Wu, Y. C.; Tsao, Y.; Wang, H. M. Voice conversion from non-parallel corpora using variational auto-encoder. Proceedings of the 2016 Asia-Pacific Signal and Information Processing
Association Annual Summit and Conference (APSIPA ASC), Jeju, Korea, 2016.
[7] Kaneko, T.; Kameoka, H.; Tanaka, K.; Hojo, N. StarGAN-VC2: Rethinking conditional methods for StarGAN based voice conversion. Proceedings of the 20th Annual Conference of the International Speech Communication Association (INTERSPEECH), Graz, Austria, 2019, 679-683.
[8] Ronssin, D.; Cernak, M. AC-VC: Non-parallel low latency phonetic posteriorgrams based voice conversion. Proceedings of the 2021 IEEE Automatic Speech Recognition and Understanding Workshop (ASRU),
Cartagena, Colombia, 2021, 710-716.
[9] Saeki, T.; Saito, Y.; Takamichi, S.; Saruwatari, H. Real-time, full-band, online DNN-based voice conversion system using a single CPU. Proceedings of the 21st Annual Conference of the International SpeechCommunication Association (INTERSPEECH), Shanghai, China, 2020, 1021-1022.
[10] Arakawa, R.; Takamichi, S.; Saruwatari, H. TransVoice: Real-time voice conversion for augmenting nearfield speech communication. Proceedings of the 32nd Annual ACM Symposium on User Interface Software
and Technology (UIST), New Orleans, LA, 2019, 33–35.

[11] Nishimura, M.; Tanaka, T.; Shiratori, K.; Sakurama, K.; Nishida, S. Development of a voice shutter (Phase
1: A closed type with feed forward control). Proceedings of the 43rd International Congress on NoiseControl Engineering (INTERNOISE), Melbourne, Australia, 2014, 1291-1299.
[12] Shi, C.; Jia, Z.; Xie, R.; Li, H. An active noise control casing using the multi-channel feedforward control
system and the relative path based virtual sensing method. Mechanical Systems and Signal Processing, 144(106878), 2020.
[13] Shi, C.; Du, F.; Liu, C.; Li, H. Differential error feedback active noise control with the auxiliary filter
based mapping method. IEEE Signal Processing Letters, 29, 2022, 573-577.
[14] Tobing, P. L.; Toda, T. Low-latency real-time non-parallel voice conversion based on cyclic variational
autoencoder and multiband WaveRNN with data-driven linear prediction. Proceedings of the 11th ISCA
Speech Synthesis Workshop, Budapest, Hungary, 2021, 142-147.
[15] Tobing, P. L.; Toda, T. High-fidelity and low-latency universal neural vocoder based on multibandWaveRNN with data-driven linear prediction for discrete waveform modeling. Proceedings of the 22nd Annual
Conference of the International Speech Communication Association (INTERSPEECH), Brno, Czechia, 2021,
2217-2221.
[16] Zhao, Y.; Huang, W. C.; Tian, X.; Yamagishi, J.; Das, R. K.; Kinnunen, T. H.; et al. Voice conversion challenge 2020: Intra-lingual semi-parallel and cross-lingual voice conversion. Proceedings of the Joint
Workshop for the Blizzard Challenge and Voice Conversion Challenge 2020, Shanghai, China, 2020, 80–98.
[17] Kubichek, R. Mel-cepstral distance measure for objective speech quality assessment. Proceedings of the1993 IEEE Pacific Rim Conference on Communications Computers and Signal Processing, Victoria, Canada,
1993, 125-128.
[18] Lo, C. C.; Fu, S. W.; Huang, W. C.; Wang, X.; Yamagishi, J.; Tsao, Y.; et al. MOSNet: Deep learning based objective assessment for voice conversion. Proceedings of the 20th Annual Conference of theInternational Speech Communication Association (INTERSPEECH), Graz, Austria, 2019, 1541-1545.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0703

Road profile based road active noise control
Hakjun LEE1; Youngjin PARK2
1

KAIST, Republic of Korea

2

KAIST, Republic of Korea

ABSTRACTPowertrains for the automobile are changing from internal combustion engines to electric motors.
Transformation of powertrains causes a significant reduction of engine noise inside the vehicle cabin and in
results, the road noise has increased relatively. For better NVH performance, automobile companies are
adopting active noise control to reduce the road noise inside the vehicle cabin. However, due to complex
propagation path and numerous sensors and actuators, adaptation algorithm for the ANC requires significant
amount of time and computational complexity for the weight filters to become converged. This study
proposed road profile-based road active noise control. Instead of updating the weight filters adaptively, byutilizing the road profile information gathered preliminarily, the weight filters are updated instantly into the
optimal filters. Performance of the proposed algorithm will be compared with the traditional MIMO FxLMS
algorithm with respect to the noise reduction performance and convergence speed.
Keywords: Active noise control, Road noise, Road profile, Vehicle NVH

1. INTRODUCTION
As the trend of the powertrains for the automotive vehicles is changing from the use of internal
combustion engines to electric motors, the NVH(Noise, Vibration, and Har shness) characteristics ofthe vehicle is also changing. The interior noise for the vehicle was mainly composed of engine noisefor the vehicle with the internal combustion engines. However, as the internal combustion engine is
now substituted to the electrical motor, the noise from the powertrain is reduced dramatically, and theinterior noise due to road noise is now become the major noise source. The road noise was reduced
by adding the sound absorption materials to the vehicle, but it had limitations due to its mass and cost.
Vehicle companies are now interested in the active noise control to reduce the road noise. Active noise
control was first introduced by Lueg in 1930s [1]. With the development of fine performance of digital
signal processor(DSP), it has been used not only for the headphones, but also for the vehicle noise
reduction, especially the engine noise. The engine noise is tonal noise with low frequency band, andwas easy to capture the reference signal [2] [3]. In comparison, active noise control for the road noise
was introduced recently [4] due to complex noise propagation path and difficulty of measuring thenoise signal.

2. RESEARCH OBJECTIVES
While the vehicle is travelling on the different types of road pavement, the noise inside the vehicle
and the vibration measured from the chassis shows different characteristic ass shown in Figure 1 andFigure 2 . In results, the optimal weight filters to reduce the road noise inside the vehicle using thevibration signal as the reference signal, shows different characteristic when the vehicle is travellingat different road type with same vehicle speed. Consequently, as the vehicle is travelling at different
road type, the weight filter for the ANC controller is also trying to converge to the new optimal filter
which results the poor road noise reduction performance. Therefore, the controller must find out the
newly changed road type and updates the weight filter to the new optimal filter to reduce the1hj.lee.sdac@kaist.ac.kr

2

yjpark@kaist.ac.kr

Figure 1 Noise spectrograms for different road typeFigure 2 Vibration power spectrum for different road typeconvergence time and produces better noise reduction performance.
Road classification will be performed by road profile transformantion using the vibration signal
measured from the chassis of the vehicle. Using the quarter car model, the road profile is estimatedindependent of the vehicle travelling speed. Then the classification of the road is performed using the
spatial PSD of road profile.
After the road classification is performed, weight update is performed by using the Kronecker
product decompostion. The optimal weight filter is estimated rather in adaptive ways, whichguarantees better noise reduction performances.

3. ROAD NOISE ACTIVE NOISE CONTROL
3.1

System configuration

Figure 3 System configuration

System configuration of the road noise active noise control is shown in Figure 3. The vibration ismeasured at the chassis of the vehicle and used it as road profile estimation and the reference signal
for the ANC system. The control signal is generated through the built-in speakers at the door panelsof the vehicle. The noise signal is measured by each ear positions at the front and rear right seats.
Data was measured by travelling at different road and used it as simulation.
3.2 Road profile estimation
The road profile is estimated using the vibrations signal and the quarter car model. The road profile
is defined as the vertical displacement along the distances. It is estimated from the acceleration byusing the Figure 4, and Eq. 1. Then the spatial power spectral density of the road profile can be
estimated.

Figure 4 Quarter car model for the road profile estimation

Eq. 1
𝑦𝑟𝑜𝑎𝑑 (𝑠)=𝑣̇𝑢 (𝑠)𝑚𝑠 𝑚𝑢𝑠 𝑠 4 + (𝑚𝑠 𝐵𝑠 + 𝑚𝑢𝑠 𝐵𝑠 )𝑠 3 + (𝑚𝑠 𝐾𝑠 + 𝑚𝑠 𝐾𝑡 + 𝑚𝑢𝑠 𝐾𝑠 + 𝐵𝑠2 − 𝐵𝑠2 𝑚𝑢𝑠 ⁄𝑚𝑠 )𝑠 2+(𝐵𝑠 𝐾𝑠 + 𝐵𝑠 𝐾𝑡 − 𝐵𝑠 𝐾𝑠 𝑚𝑢𝑠 ⁄𝑚𝑠 )𝑠 + 𝐾𝑠 𝐾𝑡
𝑚𝑠 𝐾𝑡 𝑠 4 + 𝐵𝑠 𝐾𝑡 𝑠 3 + 𝐾𝑠 𝐾𝑡 𝑠 2

Figure 5 and Figure 6 each shows the power spectrum using the vibration signal and spatial powe r
spectral density using the estimated road profile. It is represented as the spatial frequency(cycles/m )versus the power spectral density(m3 ) plot. Each graph was plotted by mean and standard deviationof PSD measured from 4 different acceleration sensors of 3 different vehicle travelling speed. By
representing the road profile spatial PSD using the road profile rather using raw data of vibration
signal, it is more clustered regardless of its sensor position or travelling speed, which makes easier to
use as source data for the road classification.

Figure 5 Power spectrum using the vibrations
signalFigure 6 Spatial power spectral density using
the estimated road profile

Optimal filter derivation

3.3

Figure 7 Block diagram of ANC system
Table 1 Nomenclatures for the block diagram𝑥vibration signal measured from accelerometers𝑦control signal at the error microphone𝑦̂estimated control signal𝑑noise signal measured from microphone𝑑̂

estimated noise signal𝑒error signal measured from error microphone𝑆

secondary path between speakers and microphones

𝑆̂

secondary path model𝑃

primary path between the reference sensor and error microphone𝑊weight filter for the controller

The block diagram of ANC system can be represented as Figure 7. The optimal filter can be derived
using the auto-correlation matrix of filtered reference signal, and the cross-correlation vector offiltered reference signal and the estimated noise signal. Paleologue et al. showed that the optimal filter
derivation using a Kronecker product decomposition is accurate compare to the conventional Wiener
filter solution for the insufficient numbers of data are available [5].

4. NUMERICAL SIMULATIONS
Numerical simulation was conducted using the data measured from the vehicle travelling atdifferent road type. Figure 8 and Figure 9 each shows the noise reduction performance and means
square errors for condition that the vehicle is travelling from the quieter road to the louder road. Blueline shows the SPL of the road noise which is not reduced by ANC. Green, yellow, and purple eachshows the noise level after the ANC is performed that road was unclassified, weight was updated with
Wiener filter solution help of road classification, and the updated with proposed algorithm with thehelp of road classification. As the noise reduction performance graph shows, with the change of roadtype, proposed algorithm showed better noise reduction performance compared to the result with thecase of road type was unclassified, and the weight filter update with Wiener filter solution. MSE curve

supports the argument that the convergence speed of controller is much faster than the other case.

Figure 8 Noise reduction performance for vehicle travelling from quieter road to louder road

Figure 9 Mean square errors for vehicle travelling from quieter road to louder road

Figure 10 and Figure 11 shows the same simulation results while the vehicle was travelling from the louder
road to the quieter road. Both noise reduction performance and the MSE curve shows that the proposed
algorithm was able to reduce the road noise with the faster convergence speed.

5. CONCLUSIONS
Active noise control for the road noise had a room to improve its performance in both noise
reduction, and the convergence manner. In this study, the by adopting the road classification using theestimated road profile, the time for the weight filter to newly converge due to road change is reduced
by updating the weight filter using the optimal filter rather in adaptive ways. Also by using a
Kronecker product decomposition, the optimal filter was able to estimated with insufficient numberof data was allowed. Noise reduction performance and the MSE curve was represented to support theideas that the road noise ANC with road classification and newly proposed optimal filter estimation
had better results compared to the conventional ones.

Figure 10 Noise reduction performance for vehicle travelling from louder road to quieter road

Figure 11 Mean square errors for vehicle travelling from louder road to quieter road

ACKNOWLEDGEMENTS
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the
Korea government(MSIT) (No. NRF-2020R1A2C1012904)

REFERENCES[1] P. Lueg, "Process of silencing sound oscillations". US Patent 2,043,416, 6 1936.
[2] T. Inoue, A. Takahashi, H. Sano, M. Onishi and Y. Nakamura, "NV countermeasure technology for acylinder-on-demand engine-development of active booming noise control system applying adaptivenotch filter," in SAE Technical Paper, 2004.
[3] R. Schirmacher, R. Kunkel and M. Burghardt, "Active noise control for the 4.0 TFSI with cylinder on
demand technology in Audi's S-series," in 7th International Styrian Noise, Vibration & Harshness
Congress: The European Automtive Noise Conference, 2012.

[4] HMG Tech, "Hyundai’s World’s First Road-Noise Active Noise Control, RANC," 2022. [Online].
Available: https://tech.hyundaimotorgroup.com/article/hyundais-worlds-first-road-noise-active-noisecontrol-ranc/. [Accessed 15 4 2022].
[5] C. Paleologu, J. Benesty and S. Ciochina, "Linear system identification based on a Kronecker productdecomposition," in IEEE, 2018.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022 in Gyeongju, Korea

ABS-0788

Optimization Methods for Fixed Virtual Sensing Feedback ANC
Controllers Targeting In-Ear Headphones
Piero RIVERA BENOIS1,3; Reinhild RODEN2; Matthias BLAU2,3; Simon DOCLO1,3
1
2

Signal Processing Group, University of Oldenburg, Oldenburg, Germany

Institut für Hörtechnik und Audiologie, Jade Hochschule, Oldenburg, Germany
3

Cluster of Excellence Hearing4all, Germany

ABSTRACT
Active Noise Cancellation (ANC) applied to headphones aims at minimizing the environmental noise at thelistener’s ears. In this contribution, we consider an in-ear headphone equipped with an inner microphone andone loudspeaker and we compare different virtual sensing approaches (remote microphone technique, virtual
microphone arrangement) to derive a fixed feedback ANC controller, minimizing the sound pressure at theear drum instead of at the inner microphone. Based on multiple measurement sets of the acoustic paths
between the loudspeaker, the noise source and the ear drum, we derive robust optimization methods tocompute the FIR filter coefficients of the ANC controller, minimizing the power spectral density at the ear
drum subject to design and stability constraints. Simulation results for diffuse noise and considering multiple
reinsertions of the in-ear headphone show an improvement of the noise attenuation at the ear drum using thevirtual sensing approaches, when compared to a classical approach optimized at the inner microphone.
Keywords: Virtual Sensing, Active Noise Cancellation, Headphones

1. INTRODUCTION
Active Noise Cancellation (ANC) applied to headphones aims at minimizing the environmental
noise at the listener’s ears. The working principle of ANC is based on the destructive superposition ofsound waves, in this context the sound wave of the environmental noise reaching the listener’s ear
and the sound wave generated by the loudspeaker of the headphone (see the overview paper in [1]).
In this paper we consider an in-ear headphone with an inner microphone and one loudspeaker and weaim at minimizing the sound pressure at the ear drum by means of a fixed feedback ANC controller.
Since the sound pressure at the inner microphone and the ear drum are not equal [7], several virtual
sensing techniques have been proposed (see the literature review in [5]) that exploit measurements
performed during a calibration stage to move the zone of quiet from the position of the inner
microphone to the position of the ear drum. In [2] a convex optimization method was proposed toderive the FIR filter coefficients of the ANC controller using the virtual microphone arrangement(VMA) approach, exploiting the proximity of the inner microphone to the ear drum to minimize thesound pressure at the ear drum. In [6],[7] non-convex optimization methods were proposed to derive
the IIR filter coefficients of the ANC controller using the remote microphone technique (RMT)
approach, relying only on the coherence between the sound pressure at the positions of the inner
microphone and the ear drum to minimize the sound pressure at the ear drum.
In this work, we propose two convex optimization methods to derive the FIR filter coefficients of
the ANC controller using the RMT and VMA approaches, which are robust against reinsertions of theheadphones. Additionally, we show that the VMA approach [2] and the (non-virtual-sensing)minimum variance control (MVC) approach [3] are special cases of the proposed RMT approach.
This paper is structured as follows: Firstly, a description of the virtual sensing technique used inthis work will be presented. Secondly, the proposed optimization methods for the design of the ANC
controllers are described. Fourthly, simulations results based on acoustic transfer functions measured
with an in-ear headphone prototype are presented to validate the proposed optimization methods.
1piero.rivera.benois@uni-oldenburg.de2. FEEDBACK VIRTUAL SENSING
The virtual sensing algorithms that we consider use a two-stage approach (see Figure 1) . In thefirst stage, called calibration stage, a probe tube microphone (PTM) is placed at the ear drum.
Afterwards, the in-ear headphone is inserted into the ear canal and the acoustic path between the
loudspeaker and the ear drum, called the secondary path 𝑆(𝑧) , is measured. Subsequently, â (𝑧) =
calibration noise field is generated around the user to measure the transfer fun ction 𝑀̂̂̂̂Φ𝑑𝑟 (𝑧)⁄Φ𝑟𝑟 (𝑧) between the inner microphone and ear drum, where Φ𝑑𝑟 (𝑧) and Φ𝑟𝑟 (𝑧) denote thecross- and auto-correlation functions in the z-transform domain estimated from the signals measured
at the inner microphone and the PTM (ear drum). After removing the PTM, the in-ear headphone isreinserted and the acoustic path between the loudspeaker and the inner microphone, called thefeedback path 𝐵𝑟 (𝑧), is measured.

Figure 1. On the left, an in-ear headphone with an inner microphone and one loudspeaker, 𝑟(𝑛) and 𝑑(𝑛)denote the signals generated by the incident noise arriving at the inner microphone and the ear drum,
respectively, and 𝑢(𝑛) denotes the loudspeaker signal generated by the ANC controller. On the right, theblock diagram of the proposed ANC controller implementing a virtual sensing algorithm.
During the second stage, called control stage, it is assumed that the measured acoustic paths to theear drum remain more or less unchanged after removing the PTM and reinserting the in-ear headphone.
̂ (𝑧) and 𝐵̂𝑟 (𝑧) are used as internal models 𝑆̃(𝑧), 𝑀̃ (𝑧) andThe measured acoustic paths 𝑆̂(𝑧), 𝑀
𝐵̃𝑟 (𝑧) by in the virtual sensing algorithm in Figure 1 to make an on-line estimation of the soundpressure at the ear drum 𝑒(𝑛). The estimated sound pressure at the ear drum 𝑒̂ (𝑛) is used as input forthe controller 𝑊(𝑧).
The power spectral density (PSD) of 𝑒(𝑛) at frequency 𝑓 can be written as follows
22Φ𝑒𝑒 (𝑓) = (1 −

̃ (𝑓)𝑊(𝑓)𝑆(𝑓)𝑀|Φ𝑑𝑟 (𝑓)|Φ𝑑𝑟 (𝑓)) Φ𝑑𝑑 (𝑓) + |−| Φ𝑟𝑟 (𝑓).
Φ𝑑𝑑 (𝑓)Φ𝑟𝑟 (𝑓)Φ𝑟𝑟 (𝑓) 1 + 𝑊(𝑓) (𝑆̃(𝑓) + 𝑀
̃ (𝑓) (𝐵𝑟 (𝑓) − 𝐵̃𝑟 (𝑓)))The left-hand term determines the minimum achievable PSD Φ𝑒𝑒 (𝑓), which is only equal to zero
when the magnitude squared coherence between 𝑟(𝑛) and 𝑑(𝑛) is equal to 1. The right-hand term
defines the scope of the optimization, where it should be noted that both numerator as well as
denominator depend on the controller 𝑊(𝑓).
For the virtual sensing approaches (RMT and VMA) it is assumed that the secondary path 𝑆(𝑧)remains unchanged after removing the PTM and reinserting the in-ear headphone. In addition it isassumed that the changes in the feedback path 𝐵𝑟 (𝑧) can be compensated with state-of-the-art on-line
estimations methods. When using the RMT approach, it is assumed that for the external noise source
the sound pressure at the inner microphone and the ear drum are related by 𝑑(𝑛) = 𝑚(𝑛) ∗ 𝑟(𝑛), andΦ𝑑𝑟consequently,= 𝑀(𝑓), such that if these assumptions are applied to the previous equation, theΦ𝑟𝑟

PSD at the ear drum Φ𝑒𝑒 simplifies to

2
𝑊(𝑓)𝑆̃(𝑓)| Φ𝑟𝑟 (𝑓).
1 + 𝑊(𝑓)𝑆̃(𝑓)Alternatively, when using the VMA approach, it is assumed that for the external noise source the
RMT
̃ (𝑓)
Φ𝑒𝑒
(𝑓) = |𝑀(𝑓) − 𝑀sound pressure at the inner microphone and at the ear drum are equal, i.e. 𝑑(𝑛) = 𝑟(𝑛). Hence, thẽ (𝑧) in Figure 1 is set to 𝑀
̃ (𝑧) = 1 and the PSD at the ear drum reduces tointernal model 𝑀
21VMAΦ𝑒𝑒 (𝑓) = || Φ𝑟𝑟 (𝑓).
1 + 𝑊(𝑓)𝑆̃(𝑓)In contrast to the virtual sensing approaches, when using the (non-virtual-sensing) MVC approach, it
is assumed that the secondary and feedback paths are equal, i.e. 𝑆(𝑧) = 𝐵𝑟 (𝑧) and, therefore, theinternal models −𝑆̃(𝑧) and 𝐵̃𝑟 (𝑧) in Figure 1 are removed and the PSD at the ear drum reduces to2
1
MVC (𝑓)Φ𝑒𝑒= || Φ𝑟𝑟 (𝑓),1 + 𝑊(𝑓)𝐵̃𝑟 (𝑓)which is equal to the PSD at the inner microphone. As can be observed from the last three equations,
RMT
the optimization of the controller 𝑊(𝑧) by minimization of the objective functions Φ𝑒𝑒
(𝑓) ,
VMA
MVC
Φ𝑒𝑒 (𝑓) and Φ𝑒𝑒 (𝑓) is a non-convex optimization problem, because the denominators depend on
the controller 𝑊(𝑓). Instead of directly minimizing the objective functions, we propose to deri ve thecontroller 𝑊(𝑧) by satisfying the optimality conditions resulting in the minimum achievable PSD atthe ear drum. For the RMT approach, the optimality condition |𝑊(𝑓)𝑆̃(𝑓)| ≫ 1 results in theminimum achievable PSD
RMT,opt
̃ (𝑓)|2 Φ𝑟𝑟 ,Φ𝑒𝑒(𝑓) = |𝑀(𝑓) − 𝑀̃ (𝑓) and the real system 𝑀(𝑓). For thewhich depends on the similarity between the internal model 𝑀
VMA approach, the optimality condition |1 + 𝑊(𝑓)𝑆̃(𝑓)| ≫ 1 results in the minimum achievable
PSD
VMA,optΦ𝑒𝑒(𝑓) = 0.
Similarly, for the MVC approach the optimality condition |1 + 𝑊(𝑓)𝐵̃(𝑓)| ≫ 1 results in theminimum achievable PSD
MVC,optΦ𝑒𝑒(𝑓) = 0.

3. CONTROLLER DESIGN
RMTInstead of deriving the controller 𝑊(𝑧) by minimizing the non-convex objective functions Φ𝑒𝑒
,
VMA
MVC
Φ𝑒𝑒 and Φ𝑒𝑒 , we propose to satisfy the optimality conditions presented in the previous section as
well as possible, resulting in convex optimization problems in the discrete Fourier transform (DFT)domain. We assume 𝑊(𝑧) to be an FIR filter with N filter coefficients stacked in the vector 𝒘. For
the RMT controller, the optimality conditions to be satisfied is |𝑊(𝑓)𝑆̃(𝑓)| ≫ 1 , resulting in theconvex maximization problem in the DFT domain

𝒘RMT = arg max ∑
𝒘

𝐿𝐷𝐹𝑇
−1
2
𝑘=0

2

2

̃ (𝛺𝑘 )| 𝐺12 (𝛺𝑘 ),|𝑊(𝛺𝑘 )𝑆̃(𝛺𝑘 )| |𝑀

where 𝑆̃(𝛺𝑘 ) is the frequency responses of the secondary path internal model 𝑆̃ (𝑧), 𝑘 denotes thefrequency index, 𝐿𝐷𝐹𝑇 denotes the DFT length, 𝐺1 (𝛺𝑘 ) denotes a frequency dependent function toweight the low frequencies more than the mid and high frequencies and the squared magnitude
̃ (𝛺𝑘 )|2 is used to weight lower the frequencies that are attenuatedresponse of the internal model |𝑀by 𝑀(𝑧) . For the VMA and MVC controllers, the optimality condition to be satisfied is|1 + 𝑊(𝑓)𝑆̃(𝑓)| ≫ 1 and |1 + 𝑊(𝑓)𝐵̃𝑟 (𝑓)| ≫ 1 , respectively. Hence, as in [2] and [3] thecorresponding convex maximization problems can be formulated as
𝒘VMA = arg max ∑
𝒘

and

𝐿𝐷𝐹𝑇
−1
2
𝑘=0

𝒘MVC = arg max ∑𝒘

2|1 + 𝑊(𝛺𝑘 )𝑆̃(𝛺𝑘 )| 𝐺12 (𝛺𝑘 )

𝐿𝐷𝐹𝑇
−1
2

𝑘=0

2

|1 + 𝑊(𝛺𝑘 )𝐵̃𝑟 (𝛺𝑘 )| 𝐺12 (𝛺𝑘 ).

̃ (𝛺𝑘 ),It should be noted that the VMA and MVC approaches do not require the frequency response 𝑀
and, therefore, their calibration stage does not require a calibration noise field. Moreover, the MVC
approach only requires 𝐵̃𝑟 (𝛺𝑘 ), hence, no PTM is needed for its calibration stage.
Aiming at deriving a controller 𝑊(𝑧) that yields a stable system, a stability constraint is imposed.
Similarly as in [2], the solution space is restricted by a single-sided hyperbolic boundary. However,aiming at producing a quadratic dependency w.r.t. 𝑊(𝛺𝑘 ), we propose to formulate the stability

constraint as an inequality between quadratic terms as22|𝜚 − 𝑊(𝛺𝑘 )𝑆̃(𝛺𝑘 )| ≤ (|𝜚 + 𝑊(𝛺𝑘 )𝑆̃(𝛺𝑘 )| + 2 ⋅ 𝜌) ,where 𝜚 determines the focus (−𝜚, 0) and 𝜌 the x-axis intersect (−𝜌, 0) of the hyperbola. In
addition, in order to limit the maximum gain of the controller 𝑊(𝑧), the convex inequality constraint|𝑊(𝛺𝑘 )|2 ≤ 𝐺32 (𝛺𝑘 )is introduced, where 𝐺3 (𝛺𝑘 ) denotes the maximum allowed gain. Feedback ANC approaches are
generally subject to the water-bed effect and therefore prone to produce amplifications outside theattenuation bandwidth [7]. Aiming at restricting such amplification, we propose to introduce thefollowing convex inequality constraint2̃ (𝛺𝑘 )
2
𝑀
̃
)𝑆
(𝛺
)
+
𝑊(𝛺
(1
−
)|
≤ 𝐺22 (𝛺𝑘 )|1 + 𝑊(𝛺𝑘 )𝑆̃(𝛺𝑘 )|
|1
⁄̂
𝑘
𝑘
𝑀(𝛺𝑘 )
for the optimization of the RMT controller, where 𝐺2 (𝛺𝑘 ) denotes the maximum allowed̃ (𝛺𝑘 ) and 𝑀̂ (𝛺𝑘 ) are considered. Since for the VMA
amplification and differences between 𝑀
̃
̂
(𝛺
)
(𝛺
)
controller the frequency responses 𝑀 𝑘 and 𝑀 𝑘 are set to 1, the previous inequality constraint
reduces to2
1 ≤ 𝐺22 (𝛺𝑘 )|1 + 𝑊(𝛺𝑘 )𝑆̃(𝛺𝑘 )| .
Similarly, for the optimization of the MVC controller, 𝑆̃(𝛺𝑘 ) is replaced by 𝐵̃𝑟 (𝛺𝑘 ) in this constraint,i.e.
2
1 ≤ 𝐺22 (𝛺𝑘 )|1 + 𝑊(𝛺𝑘 )𝐵̃𝑟 (𝛺𝑘 )| .
The proposed convex maximization problems subject to the aforementioned constraints can thenbe solved using SQP algorithms, e.g., implemented in the MATLAB function fmincon(). During all
optimizations in this work we used 𝑁 = 128 filter coefficients, 𝐿𝐷𝐹𝑇 = 8192, 𝜚 = 0.8 and 𝜌 = 0.9.
Similarly to [2], we used the frequency-dependent functions 𝐺1 (𝑓) , 𝐺2 (𝑓) and 𝐺3 (𝑓) depicted in
Figure 2.

Figure 2. Frequency-dependent functions: 𝐺1 (𝑓) is the frequency-weighting function used in the objectivefunction, 𝐺2 (𝑓) is the maximum allowed amplification of 4 dB due to water-bed effect and 𝐺3 (𝑓) is the
maximum controller gain of 26 dB in the low frequencies.

4. SIMULATIONSIn this section, the performance of the proposed RMT and VMA controllers is compared to theperformance of the MVC controller for a diffuse noise field using the inner microphone and one
loudspeaker of the in-ear headphone prototype described in [4]. The acoustic transfer functions
between the loudspeakers and the inner microphone 𝐵𝑟 (𝑧) and the ear drum 𝑆(𝑧) were measured in[4] for several reinsertions of the in-ear headphone prototype in the ear of a subject using a probe tube
microphone. All simulations were performed at a sampling frequency of 𝑓𝑠 = 44.1 kHz. From thedatabase in [4] eight measurement sets were considered. Using one measurement set, the measured
secondary path 𝑆̂(𝑧) was used and a diffuse calibration noise field was generated to determine thê (𝑧) = Φ̂ 𝑑𝑟 (𝑧)⁄Φ̂ 𝑟𝑟 (𝑧). The RMT controller was optimized considering using thetransfer function 𝑀
̂ (𝑧), whereas the VMA controller was optimized using only the transfer
transfer functions 𝑆̂(𝑧) and 𝑀
function 𝑆̂(𝑧) . Using the remaining seven measurement sets, seven reinsertions of the in -earheadphone were simulated. After each reinsertion, the MVC controller was re-optimized consideringa perfect measurement of the respective feedback path, i.e. 𝐵̂𝑟 (𝑧) = 𝐵𝑟 (𝑧). For each reinsertion acontrol stage of the RMT, VMA and MVC controllers was simulated. For the RMT control stage all̃ (𝑧) and 𝑆̃(𝑧) in Figure 1 are required. For the VMA control stage only
three internal models 𝐵̃𝑟 (𝑧), 𝑀̃ (𝑧) is set to one. For the MVC control stage no internal𝐵̃𝑟 (𝑧) and 𝑆̃(𝑧) are required, because 𝑀
model is required. For the RMT and VMA control stages, the internal model of the feedback path was
assumed to be perfect, i.e. 𝐵̃𝑟 (𝑧) = 𝐵𝑟 (𝑧). The internal model of the secondary path was set to thẽ (𝑧) wassecondary path measured during the calibration stage, i.e. 𝑆̃(𝑧) = 𝑆̂(𝑧). The internal model 𝑀̂derived using a causal FIR approximation [8] of the transfer function 𝑀(𝑧) determined during thecalibration stage.

(a)

(b)
(c)
Figure 3. Simulation results for (a) the MVC controller, (b) the VMA controller and (c) the RMT controller.
ANCoff and ANCon correspond to PSDs at the ear drum when ANC is turned off and on, respectively.
Attenuation ± σ corresponds to the mean attenuation curve alongside the standard deviation calculatedusing seven reinsertions of the in-ear headphone in [4].
Figure 3 depicts the PSDs of the sound pressure at the ear drum Φ𝑒𝑒 (𝑓) with ANC off and ANCon, using either the MVC, the VMA or the RMT controller. In the same plot the mean attenuation
curve is presented alongside the standard deviation calculated using the seven reinsertions. Please
note that when the mean attenuation is smaller than 0 dB attenuation is produced and, otherwise,
amplification is produced instead. In addition, it should be noted that none of the re-insertions
produced an unstable system, which corroborates that the proposed optimization method yields arobust controller. First, it can be observed from ANC off that the passive attenuation of the in -earheadphone is very high for frequencies above 4 kHz. Second, it can be observed in Figure 3 (a) thatthe attenuation achieved by the MVC controller is limited to the bandwidth between 200 to 550 Hzwith a maximum magnitude of approx. 10 dB. In the frequency regions before and after the attenuation
bandwidth a water-bed effect is visible, which exceeds the limit of 4 dB imposed by 𝐺2 (𝑓) at about
1.5 kHz. This may be due to the fact that the assumptions of the MVC approach do not hold for
frequencies above 1 kHz. Third, it can be observed in Figure 3 (b) that the attenuation achieved by
the VMA controller is much higher both in terms of bandwidth and magnitude when compared to the
MVC controller. Furthermore, although the water-bed effect is controlled for frequencies below 4 kHz,amplifications of up to 25 dB can be observed at higher frequencies. This may be due to the fact thatthe assumption of the MVA controller, i.e. 𝑑(𝑛) = 𝑟(𝑛) , does not hold in this frequency region,because the wave lengths are comparable to the distance between the inner microphone and the ear
drum. Finally, it can be observed in Figure 3 (c) that the attenuation achieved by the RMT controller
is slightly inferior when compared to the attenuation achieved by the VMA controller. However, thewater-bed effect produced in the high frequencies is much lower when compared to the water -bed
effect produced by the VMA controller. The fact that the water-bed effect is still higher than 4 dB may
be due to the variability of the system 𝑀(𝑧) in the high frequencies.

5. CONCLUSIONSIn this paper, we considered an in-ear headphone equipped with an inner microphone and one
loudspeaker and proposed two optimization methods based on the RMT and VMA approaches toderive a fixed feedback ANC controller, minimizing the sound pressure at the ear drum instead of at
the inner microphone. The optimization methods require a calibration stage during which a PTM isinserted into the ear and the acoustic paths between the loudspeaker, the noise source and the ear drum
are measured. We proposed to use optimality conditions to formulate convex objective functions
resulting in the minimum achievable PSD at the ear drum, subject to convex stability and design
constraints. Furthermore, aiming at a better control of the water-bed effect in the high frequencies, a
new constraint was proposed for the optimization of the RTM controller. The new constraint exploits
the acoustic path measured between the inner microphone and the ear drum with an external
calibration noise field. Simulation results for diffuse noise and considering multiple reinsertions of
the in-ear headphone corroborated that the ANC controllers derived with the proposed optimization
methods are robust against reinsertions of the device. A considerable improvement of the noise
attenuation at the ear drum could be observed when comparing the RMT and VMA approaches to theclassical MVC approach optimized at the inner microphone. While the RMT controller achieves abetter control of the amplification outside of the attenuation bandwidth when compared to the VMA
controller, the VMA controller achieves the highest attenuation bandwidth an d magnitude among theevaluated controllers. In future work the optimization methods will be extended for in-ear headphones
with multiple loudspeakers, and by integrating uncertainty models of the acoustic transfer functions,e.g., produced by intra-subject variability.

ACKNOWLEDGEMENTSs
This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany's Excellence Strategy - EXC 2177/1 - Project ID 390895286 and Project
ID 352015383 - SFB 1330 C1.

REFERENCES
1. Kajikawa, Y., Gan, W., & Kuo, S. (2012). Recent advances on active noise control: Open issues andinnovative applications. APSIPA Transactions on Signal and Information Processing, 1, E3.
doi:10.1017/ATSIP.2012.4.
2. P. Rivera Benois, R. Roden, M. Blau, and S. Doclo. Optimization of a fixed virtual sensing feedback anc
controller for in-ear headphones with multiple loudspeakers. In Proc. IEEE International Conference on
Acoustics, Speech and Signal Processing (ICASSP), pages 8717–8721., 2022.
3. P. Rivera Benois. Hybrid and Pseudo-Cascaded Active Noise Control Applied to Headphones. PhD thesis,
Helmut-Schmidt-Universität / Universität der Bundeswehr Hamburg, Hamburg, December 2020.
4. F. Denk and B. Kollmeier. The hearpiece database of individual transfer functions of an in-the-ear earpiecefor hearing device research. Acta Acust., 5:2, 2021.
5. D. Moreau, B. Cazzolato, A. Zander, and C. Petersen, A review of virtual sensing algorithms for active
noise control, Algorithms, vol. 1, p. 69–99, Nov 2008.
6. Z. Zhang, M. Wu, L. Yin, C. Gong, J. Wang, S. Zhou, J. Yang, Robust feedback controller combined withthe remote microphone method for broadband active noise control in headrest, Applied Acoustics, Volume
195, 2022.
7. F. An, Q. Wu, and B. Liu, Feedback controller optimization for active noise control headphones
considering frequency response mismatch between microphone and human ear, Applied Sciences, vol. 12,
no. 3, 2022.
8. P. Rivera Benois, P. Bhattacharya, and U. Zölzer, Derivation technique for headphone transfer functions
based on sine sweeps and least squares minimization, In Proc. INTER-NOISE and NOISE-CON Congress
and Conference, vol. 253, no. 4, 2016.

ABS-0946

New applications of AI techniques for nonlinear control of loudspeakers
Pascal BRUNET(1) , Yuan LI(1) , Felix KOCHENDÖRFER(1) , Glenn KUBOTA(1)(1) Samsung Research America, USA, p.brunet1@samsung.com, yuan.l@samsung.com

ABSTRACT
To obtain high loudness with good bass extension, while keeping distortion low, and ensuring mechanical protection, the motion of the loudspeaker diaphragm needs to be controlled accurately. We have shown in a previous
paper that machine learning is a viable approach to “invert” a loudspeaker, recovering voltage input from observed excursion of diaphragm. This opens the possibility of controlling and linearizing diaphragm motion
using a neural network as an alternative to model-based nonlinear methods. This technique allows control andlinearization of the loudspeaker without theoretical assumptions. In this paper, we consolidate our previous
results by improving the data quality and statistical distribution for better training. We further explore othernetwork architectures, more elaborate than our initial single-layer feed-forward network.

Keywords: nonlinear control, AI, machine learning, loudspeaker, distortion

1

INTRODUCTION

Loudspeakers have been long known to be a potential source of nonlinear distortion. This is typically a resultof multiple nonlinearities within the electrodynamic transducer. Several parameters of the transducer, such as
the motor’s force factor Bl, the mechanical stiffness of the suspension Kms and the voice coil inductance Le arehighly dependent on the cone excursion and thus the amplitude of the input signal, as shown in Fig. 1. As
a result, the reproduction of an audio signal becomes less accurate with increasing level. This can become aproblem in compact speaker systems which are intended to use the full excursion capability of a transducer.
There have been numerous attempts to linearize the loudspeaker response at higher excursions using integrodifferential equations [1], nonlinear state-space [2], or port-Hamiltonian systems [3]. These control systems use
physical loudspeaker models based on Thiele/Small parameters. While these model parameters can provide agood understanding about the principles and operation of a transducer, they can be limited in capturing all
characteristics of the loudspeaker, which often vary with different input signals. A major challenge of thesecontrol systems is thus to correctly estimate the individual parameters and, if the model precision is insufficient,increase the number of variables to be identified.
Artificial intelligence (AI) techniques, especially machine learning (ML), allows to escape this complexity
by relying solely on experimental data instead of a physical model. Machine Learning uses empirical blackbox models with a much larger number of parameters than what would be feasible in a physical white-box
loudspeaker model. Its generic mathematical functions allow for a more complex model with a large number ofparameters that are tuned automatically and systematically. The training is based on experimental data using test
signals that represent the typical use case of the loudspeaker in order to capture its full complexity. The use ofneural networks (NN) for linearization was already proposed about 30 years ago by Low and Hawksford [4],using a loudspeaker system with current feedback. In recent years however, the methods used to identify physical systems by machine learning have become more and more elaborate [5, 6, 7], although without applications
to electroacoustics. This paper proposes a simple feed-forward training method to derive the relationship between diaphragm excursion and input voltage. After an ideal target displacement of the loudspeaker diaphragm
is obtained by linear filtering of the music signal, the trained NN is used derive the control voltage based on
the given displacement.

6
Bl [N/A]
Kms [N/mm]
Le [100 µH]

5

4

3

2

1

0

−10

−5

0
Excursion [mm]510Figure 1. Nonlinearities arise from the driver’s Bl (electrodynamic force factor), Kms (mechanical suspension
stiffness), and Le (voice coil inductance)

2

METHODS FOR LOUDSPEAKER LINEARIZATION AND CONTROL

2.1 NN Based Control
As established in previous works [2, 8], the voltage u present at the terminals of the loudspeaker can be
expressed as a function of the displacement x and its time derivatives in the continuous domain.
In the digital domain, the voltage samples can be written as a function of L past displacement samples:u[k] = Φ(x[k], x[k − 1], x[k − 2], ...x[k − L + 1])(1)

where Φ is a nonlinear function, intrinsic to the loudspeaker and L is the depth of samples. The L past samples
describe the state of the loudspeaker.
A time-delay neural network (TDNN) to approximate Φ is an adequate method to create an AI nonlinear
control algorithm (TDNN-NLC). To train the TDNN, a generic signal is played on the loudspeaker and two setsof time-series data are recorded: an input series x[k] and an output/target series u[k], where x is the loudspeakerdisplacement measured with a laser and u is the voltage recorded at the terminals of the loudspeaker. The
TDNN is trained until it can correctly predict the values of u[k] from previous values of x[k].
After proper training, the TDNN is used as follows: a target displacement is determined from the audio
content by linear filtering [2] and the TDNN estimates the voltage to apply to the loudspeaker to obtain thattarget displacement. It is important to note that the target displacement is linearly related to the audio material.
2.2 Model-Based Control
The principle of this method is described in detail in [2]: At each time instant, that method calculates the input
voltage value that produces a targeted displacement of the membrane and thus the intended sound wave.
Model-based nonlinear control algorithm (Model-NLC):
1. Trajectory planning: target displacement x is obtained by low-pass filtering of the input signal. Some bassemphasis can be applied at that stage.
2. Target current is derived from target displacement and its derivatives: i = (Kms (x)x + Rms ẋ + Mms ẍ)/Bl(x)e (x) i)3. Nonlinear control voltage is derived from i and x: u = Bl(x)ẋ + Re i + ∂ (L∂twhere Re is the electrical resistance of the voice coil, Le (x) the electrical inductance of the voice coil, Kms (x)the stiffness of the suspension, Rms the mechanical resistance of the suspension losses, Mms the mechanicalmoving mass of the voice coil and cone, and Bl(x) the force factor of the transducer motor. As can be seen in
Fig. 1, Le (x), Kms (x) and Bl(x) are nonlinear function of the excursion x.

The control voltage will produce the target displacement under nominal conditions (exact model). A linearization of the loudspeaker is then achieved by nonlinear control of the voice coil motion. In order to havea model that best fits the actual speaker system, the physical parameters of the model were measured with a
Klippel Analyzer system with the driver mounted in the closed box. Additionally, a measurement of voltage andexcursion was then done on the system using pseudo-music. The voltage was then passed through a nonlinear
model based on the physical parameters, which gave an estimated excursion to be compared with the measured
excursion. A custom MATLAB script was used to adjust three parameters, using Nelder-Mead optimization, inorder to minimize the excursion error. These parameters were the values of Kms (x = 0) (the shape of the curve
was not changed), Rms , and Mms .
2.3 Linear Control
As a baseline, we used linear regression to estimate the input voltage from the excursion. The linear model wastrained with measured excursion and voltage using the same material as for NN training. The past excursion
samples were collected into a Toeplitz matrix T and a least-square solution was calculated for the following
equation:
T w=U

(2)

where w contains the linear weights and U is the vector of measured voltages.
The vector w was then used to estimate the control voltage to apply in order to obtain the target displacement.

3

EXPERIMENTAL RESULTS

3.1 NN Training
NN training was done with actual loudspeaker data. A 5-inch woofer in a 5-liter closed box was measured
at a 48 kHz sampling rate, using the same setup as in our previous paper [8]. The speaker was driven bya 1800 W professional power amplifier, providing enough headroom for the various excitation signals without
adding significant distortion. A National Instruments USB-4431 interface connected to a PC was used to acquiredata. A high-accuracy laser measurement sensor was used to record the cone excursion over time.
Measurement A: The DUT was measured with a 15-second pseudo-music stimulus [10], a noise that has
similar characteristics to music. The amplitude probability distribution of the stimulus is Gaussian, and thespectrum has a power distribution that follows average popular music. These two characteristics ensure large
woofer excursions for a given peak voltage with good power efficiency. It was set to a voltage level that covers
the general driver working range (a level that drives the cone excursion up to 10 mm).
Measurement B: A 60-second music clip that consists of three segments from different music genres wasused as a stimulus. Data was recorded as a test set, excluded from training, by playing the stimulus at sevenvoltage levels which resulted in peak excursions from 1 mm to 10 mm.
Pre-processing: It is crucial to train the neural network with clean data. Training data was pre-processedwith either a low-pass filter (cut-off frequency at 700 Hz) or a band-pass filter to treat measurement noise, andfurther down-sampled (by a factor of 8) for data reduction before importing to a TDNN model. System delay
was compensated using cross-correlation estimation.
Training: A depth L of 15 past excursion samples from a given time t was selected as the input delay states
for the TDNN. Tuning of the depth L was conducted as described in [8], minimizing the errors over varying L.
30 hidden nodes were used in the hidden layer. The data recordings from Measurement A at 6 kHz were used
for training the TDNN. It was divided into 70% training, 15% validation, and 15% test sets.

The TDNN model was able to recover the voltage from the recorded displacement with good precision after
training. The relative root-mean-square error (RMSE) was less than 2% between the target voltage (data from
Measurement A) and the predicted voltage, which indicated the TDNN modeled the relationship well between
the control voltage and cone displacements. Test results with Measurement B are presented in the following
section to test the model generalization further.
3.2 Model Validation
We chose sparse multitone as a stimulus for model evaluation testing. It was created with a bandwidth of 20 Hz
to 700 Hz that covers the typical range of the woofer. The tones are spaced logarithmically with frequencies thatare odd harmonics of a 5 Hz fundamental with some missing harmonics. Spaces between successive harmonics
are used to measure even- and odd-order intermodulation components produced by nonlinear distortion ([9]).
For each control model, a target displacement x(t) was determined from the multitone content by low-passfiltering, using a linear model of the loudspeaker. The Model-NLC measurement used this target directly togenerate the control voltage. The TDNN and Linear Control models used the down-sampled xds (t) as a target
to generate the control voltage to apply to the loudspeaker. Up-sampling blocks were applied for both models
in order to play back the control voltage at 48 kHz. Meanwhile the sound pressure p was captured by amicrophone placed in front of the loudspeaker at a distance of 20 mm. The diaphragm excursion was captured
by a laser sensor. The block diagram of the experimental setup is shown in Fig. 2.

u(t)Multitone[V]

Linear
Sys

x(t)
[mm]

Down
samplex_ds(t)[mm]

unn(t)AI NLC

Up
sampleDefFreq=[20 700]
Fs=48kHz[V]

Laser Sensor
ula(t)

LinearControlUpsamplepx[V]unl(t)

Model-based
NLC

[V]

Distortion
Analysis

Figure 2. Distortion Measurement Setup

3.3 Results and Discussion
We found that TDNN-NLC provides a better voltage recovery from measured excursion for all excursion ranges
as seen in Fig. 3. This is not surprising compared to Linear Control, but Model-NLC is under-performing evenwith optimized parameters. This shows the limitations of a physical model approach. The RMSE is calculated
in the time domain by comparing the measured voltage with the voltage recovered from the measured excursion
by the models.
When applying control voltage to the loudspeaker, the target excursion is achieved best with TDNN-NLC,
followed closely by Model-NLC, then Linear Control (Table 1). The peak excursion is the maximum absolute
excursion reached during the experiment and the RMSE is calculated in the time domain by comparing thetarget and measured excursions.
Fig. 4 shows the sound pressure spectra and the estimated odd and even order nonlinear distortion. Overall
distortion is lowest for TDNN-NLC, followed by Model-NLC then Linear Control. Model-NLC and Linear
Control deliver very close results. Model-NLC improves the odd distortion over Linear Control but increases
even distortion. AI improve both odd and even distortions and the overall distortion is reduced by a factor oftwo (Table 2).

Test results- estimations of input voltage

20

LinearModel-NLCAI NLC18
16

rmse [%]

14
12
10
8
6
4
2
0
0

2

4

6

8

10

12

x peak [mm]Figure 3. Voltage recovery - different models compared
Table 1. Excursion control: time domain errors - target 6 mm peak
Excursion error

Linear Control

Model-NLC

TDNN-NLC

Peak x (mm)

5.95

6.00

6.01

RMSE (%)

7.7

6.7

6.5

-60
70

10

20

70

10

Frequency [Hz]

20

-60
0

-60

0

-40

0

-40

0

-40

Frequency [Hz](a) Linear
Total distortion 6.3%

0

-20

70

-20

0

0

0

10

-20

20

Magnitude [dB]

Magnitude [dB]

20

0

20

Magnitude [dB]20

Frequency [Hz](b) Model-NLC
Total distortion 5.8%(c) TDNN-NLC
Total distortion 3.0%

Figure 4. Distortion measurements. Grey: sound pressure spectrum. Green: odd-order distortion. Red: evenorder distortion. Both odd- and even-order distortions are lower for TDNN-NLC.
Table 2. Distortion results. TDNN-NLC achieves significantly lower distortion.
Distortion (%)

Linear Control

Model-NLC

TDNN-NLC

Even

4.4

5.5

2.1

Odd

4.5

2.9

2.2

Total

6.3

5.8

3.0

4

OTHER NETWORK ARCHITECTURES

4.1 LSTM
To learn and control a time-varying loudspeaker, a Long Short-term Memory (LSTM) is a good candidate. It isable to capture long-term dependencies that are useful for modeling slow evolutions of loudspeaker parameters(e.g. time-varying stiffness of diaphragm suspension, warming, etc.) that are dependent on a long-term historyof the input signal. The LSTM cell at step n shown in Fig. 5 contains the following components: Forget Gatef (Sigmoid activation function); Candidate layer g (Tanh activation function); Input Gate i (Sigmoid activation
function); Output Gate o (Sigmoid activation function); Hidden state h; Memory state c.
The hidden state at time step (n − 1) contains the output of the LSTM layer for this time step. The cellstate contains information learned from the previous time steps. At each time step, the layer adds information
to or removes information from the cell state. The layer controls these updates using gates.
In this section, we constructed a sequence-to-sequence LSTM model. The network starts with a sequence
input layer with 10 dimensions, followed by an LSTM layer with 20 hidden units. The network ends with afully-connected layer and a regression output layer. The standard Mean Squared Error is used to calculate theperformance of the networks. It represents the average squared difference between achieved output and target
values. Training data were also extracted from Measurement A. The network trained for 15000 epochs withmini-batches of size 128 using the Adam optimizer. Mini-batch is a subset of the training set that is used
to evaluate the gradient of the loss function and update the weights. The learning rate was set to 0.08. The
gradient threshold was set to 1 to prevent the gradients from exploding. The validation result on Measurement
A has an RMSE of 3.25% between the target and the predicted voltage. Experiments with the test data from
Measurement B are shown in Fig. 7. It is noticeable that the LSTM model has lower accuracy with small
excursion peak and high excursion peak data. At the same time, training on the same amount of data took avastly more extended time than other models.
y[n]c[n-1]

c[n]
tanh

f[n]

g[n]

i[n]

h[n]

o[n]

σ

tanh

σ

σ

FC

FC

FC

FC

LSTM cellh[n-1]
x[n]Figure 5. LSTM network
x[n]-input excursion vectors; y[n]-output voltage vectors

4.2 NARX
The Nonlinear Autoregressive Network with exogenous inputs (NARX) is a recurrent dynamic network withfeedback. The NARX model is based on the linear ARX (Autoregressive with Extra Input) model, commonlyused in time-series modeling. It would be similar to the TDNN model used in the previous section but combinedwith a feedback loop of delayed outputs. In an open-loop NARX Network, it uses the actual, known previous
target value in the feedback loop. While in the closed loop, the model output of the current time step is used
as an input for the next time step. Although for the open loop structure, the input to the feedforward network ismore accurate by using the actual target value. In the real physical implementation, there are some limitations
when feeding back the system output, and not appropriate for control purposes with just a one-step-ahead
prediction. The closed form network was needed for multi-step-ahead prediction in our case.

A single hidden layer was set with 20 hidden nodes. We employed tap delays with 21 delays for the external
input and one single delay of feedback for the NARX configuration. After closing the loop of the trained net
in Fig. 6a, the closed-loop network was then retrained several times to ensure that a neural network of good
accuracy was found. Fig. 6 shows the neural network structure used in this section. During training, increasing
the number of feedback delays even had a counterproductive effect on the model performance, which suggests
a TDNN model was already sufficient to map the excursion history to voltage as described in Equation 1. In
addition, the test result using recorded data from Measurement B was also compared in Fig. 7. The NARX
model had good accuracy over all ranges of excursion. However, the TDNN still held the best performance ingeneral.
HiddenHidden

x(t)
0:20

1
y(t)

1

y(t)

w

w

1

Output

w
w
b

1

20

1

(a) NARX Open Loop(b) NARX Closed Loop

Figure 6. NARX model

Test results- estimations of input voltage

18
TDNN
LSTM
NARX

16

rmse [%]

14
12
10
8
6
4
2
0
0

2

4

6

8

1
1

20

20

y(t)

w
b

1

b
b

1

x(t)

Output

w

0:20

10

x peak [mm]Figure 7. Voltage recovery - different AI models compared12

5

CONCLUSIONSThis study has fulfilled the promises of our previous paper [8]: after improved data collection and NN training,
TDNN-NLC yielded advantageous control of loudspeaker excursion and a significant reduction of nonlinear distortion. All of that was done with a simple and light NN that is easy to implement in an embedded DSP.
We have also shown that a data-driven approach guarantees more accurate results than a physical model approach. It is also easier to tune, avoids difficult parameter measurements, and is simpler to code.
LSTM and NARX also deliver acceptable accuracy, however still not as good as TDNN. They are also inferior
in terms of training difficulty, code complexity and real-time implementation.
Future work: we will continue investigating alternative network architectures and apply TDNN-NLC to more
complex loudspeaker systems like micro-drivers and vented boxes. We will also explore sound pressure to voltage mapping that would be especially beneficial for micro-drivers where diaphragm excursion is challenging tomeasure.

ACKNOWLEDGEMENTS
Samsung Electronics and Samsung Research America supported this work. The authors would like to thankthe entire staff of Samsung’s US Audio Lab who helped with all aspects of this research, offered insightful
suggestions, and contributed to this work.

REFERENCES[1] Klippel W., The Mirror Filter-A New Basis for Reducing Nonlinear Distortion and Equalizing Response in
Woofer Systems, J. Audio Eng. Soc, 40 (9), 1992, 675–691[2] Brunet P., Kubota G.S., Nonlinear Control of Loudspeaker Based on Output Flatness and Trajectory Planning, Audio Engineering Society Convention 147, October 2019[3] Falaize A, Hélie T., Passive modelling of the electrodynamic loudspeaker: from the Thiele–Small model tononlinear port-Hamiltonian systems, Acta Acustica, 4(1), 2020
[4] Low S., Hawksford M.J., A Neural Network Approach to the Adaptive Correction of Loudspeaker Nonlinearities, Audio Engineering Society Convention 95, October 1993
[5] Carlson FB. Machine learning and system identification for estimation in physical systems. arXiv preprint
arXiv:1906.02003. 2019 Jun 5.
[6] Ljung L, Andersson C, Tiels K, Schön TB. Deep learning and system identification. IFAC-PapersOnLine.
2020 Jan 1;53(2):1175-81.
[7] Lopez R, Atzberger PJ. Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems.
arXiv preprint arXiv:2012.03448. 2020 Dec 7.
[8] Brunet P., Li Y., Kubota G.S., Mariajohn A., Application of AI techniques for Nonlinear control of loudspeakers, Audio Engineering Society Convention 151, October 2021
[9] Brunet P, Decanio W, Banka R, Yuan S., Use of Repetitive Multi-Tone Sequences to Estimate Nonlinear
Response of a Loudspeaker to Music, Audio Engineering Society Convention 143 2017 Oct 8[10] Bezzola A, Brunet P., Fully Coupled Time Domain Simulation of Loudspeaker Transducer Motors. AudioEngineering Society Convention 141 2016 Sep 20

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0966

Active noise control system with moving zone of quiet using ear
tracking device
Chi-sung OH1; Joong-Kwan KIM2; Jonggyu KANG3; Kang-duck IH1
1

Hyundai Motor Company, Republic of Korea
2

Hanseo University, Republic of Korea
3

ARE co. ltd., Republic of Korea

ABSTRACTIn the application of active noise control, the size of the control area (zone of quiet) becomes smaller as thenoise frequency band increases. Therefore, when the control target moves, it deviates from the designed zoneof quiet and a louder noise can be heard. This side effect does not appear clearly at the low frequency bands
where the wavelength is long enough to cover the movement, however in the high frequency band this effectis easily noticeable due to shortened wavelength. In this study, we propose a robust active noise control
technique that enables a moving zone of quiet in real time by tracking the location of passenger’s ears. An
image-based ear tracking system generates real time coordinates of the passenger’s ear by processing input
camera image frames. As the coordinates of the ears are identified, a multi-point virtual microphonealgorithm uses the information and moves the location of virtual error microphones to the position of the ears.
Then, a multi-point adaptive filter training system focuses control effort to the newly moved zone of quiet.
Through this process the zone of quiet moves by the tracking information of the passenger’s ear and thus theoverall control performance is enhanced.
Keywords: active noise control, ear tracking, zone of quiet, multi-point virtual microphone

1. INTRODUCTION
Active noise control (ANC) system for automotive applications was first implemented to reduce
the simple low-frequency engine noise [1]. Development of fast digital signal processors (DSPs) andadvanced algorithms have enabled the ANC system to cover wider frequency band up to 300Hz thatcovers most of the broad band road noise inside the vehicle cabin [2]. The noise spectrum inside avehicle cabin prominently audible to passengers can be categorized into road noise up to 500Hz andhigher frequency noise such as wind noise. When the noise frequency increases the wavelength of thenoise decreases thus the controllable area is also reduced due to the shortened wavelength. In general,
the size of zone of quiet is around one tenth of target noise wavelength [3,4]. Therefore, it is necessary
to develop a method to increase the size of zone of quiet in order to effectively control the highfrequency noise.
There are two possible ways to increase the size of zone of quiet. The first method is to place many
control speakers and error microphones to enlarge the zone of quiet by increasing the number of target
control points. In order to achieve larger zone of quiet through this we first need to identify theaccurate location of noise source and its transfer paths. However, it is very difficult to precisely
identify various unknown noise sources and transfer paths in the vehicle. Also placing many speakers
and error microphones is not a viable option due to cost and space constraints. The second method is
to move the zone of quiet following the movement of the passenger’s ears. A moving zone of quiet inreal time by tracking the location of passenger’s ears can have the same effect as the first method but
it requires a smaller number of speakers and microphones. Also, recent production vehicles areequipped with driver monitoring system (DMS) which can share video feed with ANC system to track
1
2

dreamocs@hyundai.com
jkwankim@hanseo.ac.kr

the location of ears by specially designed algorithms. To this end, this study shows that the zone ofquiet can be increased in size by an ANC system with moving zone of quiet using an ear tracking
device.

2. CONTROL SYSTEM AND METHODOLOGY
2.1 System Configuration and Ear Tracking System
The ANC system for this study consists of 1) a camera for generating video feed of passenger’shead, 2) a controller for signal processing to derive coordinates of the ear position of the passenger,3) an algorithm for changing target control points based on received ear coordinates, 4) accelerometers
for reference signals, 5) error microphones for measuring residual noise, and 6) an amplifier andspeakers to generate control sounds.
A time of flight (ToF) sensor is an alternative to use as a tracking device, however an RGB -IR
camera for DMS is a feasible solution to track the position of the ears due to possibility of cost
reduction by functional convergence of two different systems. The camera was installed on the crash
pad center so that both the driver and passenger could be imaged simultaneously with a single camera.
The camera is an RGB-IR camera, and it uses only IR sensor images that are robust to day and nightvisibility. The video was taken at 30 frames per second. The captured video is divided into 2D image
frames to recognize the face and facial components using a deep learning algorithm. The positions of
the facial components are computed relative to the camera's mounting position as reference
coordinates. In the case of the ears, unlike the eyes, most of the time only one side of the ear is
captured. It is possible to derive the position of the other hidden ear by recognizing the rotation of thehead. The ear position is estimated using the standard human body size, and the derived coordinates
are transmitted in real time to the ANC controller.
CameraFacial Feature Extraction

Head Tracking

Ear Tracking

Figure 1 - Ear tracking process by IR camera and tracking algorithm
2.2 ANC System with Moving Zone of Quiet
Because of the computational constraints of DSP and its memory, a total of eight representative
head positions were carefully selected to model various secondary paths for moving zone of quiet.
Considering the target control frequency, the control area was designed to have 15 cm length on one
side. The selected head positions include up/down, front/back, left/right tilt, and left/right rotation. At
each position three transfer paths have to be measured and stored in the memory to take into accountthe effect of head movement and consequent moving zone of quiet. We used a mannequin withmicrophones attached at the position of the ears to minimize the movement so that consistent transfer
function measurement is possible. A specially designed jig is also used to prevent unwanted movement
or shaking at each measurement position.

Figure 2 - Specially designed jig for noise measurement at multi position

A multi-point virtual microphone algorithm is used to realize the moving zone of quiet with pre measured secondary paths. For the cost-efficient adaptive noise control, we used NTF-FxLMS
algorithm [2]. A multi-point pre-update technology is developed and used for this study. This
technique simultaneously updates the adaptive control filters at predicted head position after
movement. This technique prevents the passengers from perceiving sudden noise difference due to thetime needed for adaptive filters to converge.
2.3 Simulation Result
In order to confirm the performance of the moving zone of quiet concept, we conducted ANC
simulations with measured secondary paths at each head position. We assumed that the position of theears can be precisely estimated using the RGB-IR camera image processing, therefore we decoupled
the ear tracking functionality to focus more on the multi-point virtual microphone algorithm.
Two cases were compared: 1) deactivated moving zone of quiet, and 2) activated moving and zoneof quiet. For the case one, control performance was 7.6dB at the control point #1 wh ereas it degraded
to 4.8dB when the head moved to the control point #2. In this case the control effort is only focusedat the control point #1 thus enough convergence time does not increase the control performance at thecontrol point #2. A 3dB difference is noticeable for standard passengers, therefore without the movingzone of quiet algorithm the passengers can experience uncomfortable sound change due to sudden
ANC performance degradation. For the case two, however, the activated moving zone of quiet
algorithm guarantees the performance at the control point #2 when the head was moved to the point#2. Pre-update algorithm gives 7.3dB reduction at the control point #2. Instant 5.8dB reduction ispossible because of the moving zone of quiet algorithm. This 1.5dB difference is not easily noticeable
for untrained passengers.
Headposition

Performance
at #1

#1

7.6dBA#2

4.8dBA

Performance at #2

Control
positionchangedInstantly

Converged--#1  #2

5.8dBA

7.3dBA

Table 1 - Control performance using the moving zone of quiet algorithm

3. CONCLUSION
In this study, we showed that the performance degradation due to the movement of the passengers
can be effectively enhanced using the ear tracking device and moving zone of quiet algorithm with amulti-point pre-update technique. This method can enhance control robustness at relatively highfrequency cabin noise which has short wavelength. The use of RGB -IR camera which is also sharedby DMS increased the feasibility of the proposed system to be implemented into production vehicles.
The following ideas were implemented, and its validity is confirmed through this study.
- An ear tracking device and processing algorithms that uses mono RGB -IR camera feed.
- A multi-point virtual microphone algorithm that enables moving zone of quiet.
- A vehicle road noise ANC system with moving zone of quiet using ear tracking system.

ACKNOWLEDGEMENTS
The authors would like to thank all the participants in this project for the discussions, experimentsupports, and result analyses.

REFERENCES
1. Elliott, S. J., (2008), A Review of Active Noise and Vibration Control in Road Vehicles, ISVR Technical
Memorandum, Institute of Sound and Vibration Research (981), University of Southampton, 1-25.
2. Oh, C., Ih, K., Lee, J., and Kim, J.-K., (2018), Development of a Mass-producible ANC System for Road
Noise, ATZ Worldwide 120 (7), Springer, 58-63.
3. Duan, J., Li, M., Lim, T. C., Lee, M. R., Cheng, M. T., Vanhaaften, W., Abe, T., (2014), Combined

Feedforward-Feedback Active Control of Road Noise Inside a Vehicle Cabin, Journal of Vibration and
Acoustics, Transactions of the ASME., 136(4), 1-8.
4. Kuo, S.M., and Morgan, D.R., (1999) Active Noise Control: A Tutorial Review, Proceeding of the IEEE,(87)6, 943~973.

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-0996

Brain Stimulation by Laser-Generated Focused Ultrasound andReal-Time Electroencephalography Monitoring
J. LEE1; D-G. PAENG1,2
1

Department of Ocean System Engineering, Jeju National University, Jeju, Korea;
2

Focused Ultrasound Foundation, Charlottesville, VA, USA;ABSTRACT
Neuromodulation has been used to treat neurological disorders. Deep brain stimulation (DBS) and vagus
nerve stimulation (VNS) have been applied to treat neurological disorders for decades. Conventionaltransducers have used continuous or long-pulse ultrasound waves for neuromodulation. Laser-generated
focused ultrasound (LGFUS) has demonstrated potential applications in precise therapeutics owing to theability to produce high-pressure, high-frequency shock waves with a tight focal spot, resulting in confined
acoustic exposure of a small area. However, few neurostimulation studies using shock waves with pulse
durations of several nanoseconds are available. This study measured real-time electroencephalogram (EEG)
signals during rat brain stimulation by LGFUS. The brain was divided into LGFUS stimulation and shamregions, and EEG signals were examined. The applied laser energy range was 250 mJ to 300 mJ, while pulse
repetition frequency was performed at 1 Hz and 2 Hz. The laser intensity and peak amplitude of the EEG
signals were directly proportional. The EEG signals responded with laser PRFs. These preliminary findings
provide the basis for applying shock waves for brain stimulation to precisely target the deep brain structures.
Keywords: Laser-generated focused ultrasound, Shock waves, EEG signals, Neurostimulation

1. INTRODUCTION
Focused ultrasound can deliver acoustic energy to various anatomical regions of the brain,including deep brain structures. Low-intensity transcranial focused ultrasound (tFUS) has shown that
acoustic pressure waves do not cause temperature elevation but stimulate brain functions without side
effects of thermal effects 1,2,3,4,5,6,7 . tFUS can provide better spatial resolution at a deeper target area
than other noninvasive technologies. The energy of pulse waves is transmitted through the skull, andthe target position can be adjusted by the phase correction of multi-element array systems. In addition,
it is possible to induce the activation or inhibition of nerves by adjusting the parameters of focusedultrasound 6,7.
Neuromodulation is used to treat neurological disorders. Focused ultrasound can deliver acoustic
energy to local regions of the brain including deep brain structures. It is possible to induce theactivation or inhibition of nerves through parameter adjustments of focused ultrasound. For the studyof nerve stimulation using ultrasound, the parameters were adjusted to produce continuous or pulse
waves with pulse durations of less than 400 ms 6. Laser-generated focused ultrasound (LGFUS)
transducers have demonstrated potential applications in targeted therapeutic ultrasound applications
owing to the ability to produce high-pressure, high-frequency shock waves with a tight focal spot.
The shock waves generated by LGFUS transducers have higher acoustic pressure than theconventional ultrasound. LGFUS transducers have demonstrated potentials in precise therapeutic
ultrasound applications 8. However, few studies have been conducted on neurostimulation by shockwaves by LGFUS. This study aims to investigate the possibility of neurostimulation by shock waves
generated from a focused CNT (fCNT)transducer. We measured and compared EEG signals in rat
brains before and after sonication.

1
2

seraph035@naver.com
paeng@jejunu.ac.kr

2. METHOD
2.1 Animal Preparation
The Jeju National University Institutional Animal Care and Use Committee (IACUC) approved thisstudy. All procedures and rat handling were performed following the ethical guidelines for animalstudies. Rats were anesthetized intramuscularly during all procedures with a mixture of Zoletil 25
mg/kg (Virbac Laboratories, France) and Rumpun 4.6 mg/kg (Bayer, Leverkusen, Germany) and weremonitored throughout the experiment. No pain or suﬀering was evident because of the procedure. A
total of 2 male Sprague-Dawley rats (450g weight, Orient Bio Inc., Seongnam, Korea) were used forthis study.
2.2 Experimental setup
The experimental setup is illustrated in Fig. 1. When the laser was applied to the fCNT transducer(F# = 0.7, focal length = 1.4 cm, immersed in water), the fCNT layer produced a shock pulse. A pulse
laser system (Tribeam, Jeisys, Medical Inc., Seoul, Korea) with a wavelength of 532 nm and energy of
250 mJ to 300 mJ was employed to generate a shock pulse with a pulse repetition frequency of 1 Hz
and 2 Hz. A needle hydrophone (NH0200, Precision Acoustics Ltd, UK) was utilized to measure theshock pulse. The hydrophone was used with a 20 dB preamplifier (HP, Precision Acoustics Ltd, UK)
powered by a DC coupler (Precision Acoustics Ltd, UK). The acoustic signal was monitored using anoscilloscope (LT354, Lecroy, New York, NY, USA).
The distance from the bottom of the transducer cap of the fCNT transducer to the focal point was 2
mm. The fCNT transducer focused on the skull surface, and the space between the rat head and thetransducer cap was filled with echo gel to irradiate shock wave. The rat was moved away from thebrain skin with the help of a mechanically operated stage by 2 mm to focus the fCNT transducer on the
rat brain. Therefore, it was possible to accurately determine the focal position for stimulating the brain
and skull surfaces.

Figure 1. Rat skull surface and brain stimulation setup using the fCNT transducer cap. Transducer cap(left). Experimental setup for shock wave stimulation of the skull surface and brain (right)

3. RESULTS AND DISCUSSION
The shock wave was generated through a CNT transducer and irradiated to the rat brain, and achange in the EEG signal was measured in real-time as shown in Figure 1. The changes of EEG
signal amplitude before and after shock wave sonication with the laser PRF 1 Hz, and the energy 350
mJ, are presented in Figure 1(a). It was found that the EEG signal, which was not observed before
the shock wave sonication, was generated at the same 1 s interval as the PRF. The intensity of the
EEG signals generated by the shock wave increased with the increase in the laser energy, as shown inFigure 1(b). Laser PRF of 2 Hz resulted in the EEG signal of 0.5s interval, as shown in Figure 1(c).

Figure 1 Real-time EEG signals generated by shock waves for brain stimulation through a CNT transducer.
(a) EEG signal from brain stimulation of shock wave at laser energy of 250 mJ and PRF of 1 Hz. (b) Laser
energy of 300 mJ and PRF of 1 Hz. (c) Laser energy of 250 mJ and PRF of 2 Hz.
Figure 2 shows the comparison between the sham control group and the brain stimulation groupof ultrasounds. EEG signals from the sham control group were measured when the laser was
generated without a CNT transducer, so it could be confirmed that it was not affected by the laser
light. Moreover, there was no real-time EEG signal response when an externally loud sound wasplayed on the rats. Therefore, the EEG signals were not from the auditory stimulation through the
ears.

(a)

(b)

(c)

Figure 2 Real-time EEG Signals before and after shock waves stimulation of rat brain (a) EEG signal before
ultrasound stimulation. (b) EEG signal upon real-time ultrasound stimulation. (c) EEG signal of shamstimulation by laser on without CNT transducer.
The amplitude of EEG signals was compared when the focal point of the shock wave was changed
from the brain surface to the cortical bone. This was performed to confirm the changes witnessed
resulting from shock wave stimulation. When the shock wave was focused on the rat's brain surface,
the amplitude size was smaller than the EEG signal from the existing stimulus. It is confirmed that the
EEG signal changed according to the stimulation cycle (1Hz) of the shock wave (Figure 3(a)). Whenthe focus of the shock wave was on the rat's cortical bone, no change was observed in the EEG signal
during the stimulation cycle (Figure 3(b)). Therefore, it was checked that the rat's EEG characteristics

were altered by the shock wave's brain stimulation.

Figure 3 Real-time EEG signal change with respect to the focal position of the shock wave. (a) EEG signal
with the shock wave focus shifted to the rat's brain surface at 250 mJ of laser energy and 1 Hz of PRF. (b)EEG signal with the focus of the shock wave shifted to the rat's cortical bone.

4. CONCLUSION
This study was performed to confirm the real-time EEG signals that change when LGFUS is
stimulated in the rat brain. The EEG signal response showed different patterns according to theparameter change of LGFUS, but did not respond to external sounds, so it was verified that thestimulation was caused by LGFUS. The brain stimulation of LGFUS with a shock pulse provides a new
insight into the mechanisms driving ultrasound-mediated neurostimulation. In the future, we will
perform behavioral analysis and EEG signal identification by stimulating LGFUS at specific locations,such as the auditory cortex of the rat brain.

ACKNOWLEDGEMENTS
The Focused Ultrasound Foundation supported this research.

REFERENCES
1. Rinaldi, Patricia C., Joie P. Jones, Frederick Reines, and LeRoy R. Price. 1991. "Modification by
Focused Ultrasound Pulses of Electrically Evoked Responses from an in Vitro Hippocampal
Preparation." Brain Research 558 (1): 36-42
2. Tyler, William J., Yusuf Tufail, Michael Finsterwald, Monica L. Tauchmann, Emily J. Olson, andCassondra Majestic. 2008. "Remote Excitation of Neuronal Circuits using Low-Intensity,
Low-Frequency Ultrasound." PloS One 3 (10): e3511.
3. Tufail, Yusuf, Alexei Matyushov, Nathan Baldwin, Monica L. Tauchmann, Joseph Georges, Anna
Yoshihiro, Stephen I. Helms Tillery, and William J. Tyler. 2010. "Transcranial Pulsed UltrasoundStimulates Intact Brain Circuits." Neuron 66 (5): 681-694.
4. Yoo, Seung-Schik, Alexander Bystritsky, Jong-Hwan Lee, Yongzhi Zhang, Krisztina Fischer,
Byoung-Kyong Min, Nathan J. McDannold, Alvaro Pascual-Leone, and Ferenc A. Jolesz. 2011.
"Focused Ultrasound Modulates Region-Specific Brain Activity." NeuroImage 56 (3): 1267-1275.
5. Fry, F. J., H. W. Ades, and W. J. Fry. 1958. "Production of Reversible Changes in the Central Nervous
System by Ultrasound." Science 127 (3289): 83-84.
6. Kim, Hyungmin, Alan Chiu, Stephanie D. Lee, Krisztina Fischer, and Seung-Schik Yoo. 2014. "Focused
Ultrasound-Mediated Non-Invasive Brain Stimulation: Examination of Sonication Parameters." Brain
Stimulation 7 (5): 748-756.
7. King, Randy L., Julian R. Brown, William T. Newsome, and Kim Butts Pauly. 2013. "Effective

Parameters for Ultrasound-Induced in Vivo Neurostimulation." Ultrasound in Medicine & Biology 39(2): 312-331.
8. Baac, Hyoung Won, Jong G. Ok, Adam Maxwell, Kyu-Tae Lee, Yu-Chih Chen, A. John Hart, Zhen Xu,
Euisik Yoon, and L. Jay Guo. 2012. "Carbon-Nanotube Optoacoustic Lens for Focused UltrasoundGeneration and High-Precision Targeted Therapy." Scientific Reports 2 (1): 1-8

PROCEEDINGS of the24th International Congress on Acoustics
October 24 to 28, 2022, in Gyeongju, Korea
Extended abstractABS-1021

VIRTUAL ACOUSTIC PROTOTYPING USING TEST BASED MODELSON PROTOTYPE VEHICLESDE KLERK, DENNIS1; HAUSSLER, MICHAEL2
1

TUDelft, VIBES.technology, Muller-BBM VAS b.v
2

VIBES.technology b.v.

ABSTRACT
Simulation serves well in the development of a complex product like a car. Is is common touse analytic and numerical models, yet measurements are (mainly) used for validation purposes.
Component Mode Synthesis has seen some use in the past but more recently, the Virtual Point
Technology (VPT), has enabled engineering to derive test based models from their (modal type)measurements. This paper briefly discussed the underlying theory of Dynamic Substructuring and
VPT method to illustrate it’s use in the development of an E-compressor.
Keywords: Virtual Acoustic Prototyping · Dynamic Substructuring · Test Based Modelling · TPA

1. INTRODUCTION
Machines, means of transportation and other products that have moving and rotating parts typicallycontain parts /components that aim to reduce vibration transfer. In general one finds that building
numerical models of these complex products and its subcomponents pose a serious difficulty into the
mid and high frequency range. As such these model become (too) costly to build and / or result in
only mediocre accuracy at best.
Hence, while typically too complex to model with numerical models only, this article discusses test based modelling, using Dynamic Substructuring and the Virtual Point Technology method. Here a
Virtual Point can be seen as the experimental equivalent of an interface node with 6 Degrees ofFreedom (DoF) on a numerical model’s interface. In this way, measurements are transformed into amodel that can be coupled to a neighboring substructure of, for example, numerical nature.
Section 2 briefly discusses the theoretical background of the techniques used. Section 3 illustrates themethod on a vehicle E-compressor. The article ends with a conclusion.

2. Theory
In the following two subsections the theory of Dynamic Substructuring and Virtual Point Technology
will be explained briefly.
2.1 Experimental Dynamic Substructuring
Dynamic Substructuring using test-based models comprises several techniques that compute theassembled system dynamics from one or more measured subsystems with others either also measured
or originating from numerical simulation. An extensive explanation can be found in (1). For the sakeof convenience below one finds a short recap of the method specifically written for the coupling of 2
subsystems. The derivation starts from the dual formulation with Lagrange Multipliers:

1
2

ddeklerk@vibestechnology.com
mhaussler@vibestechnology.com

Here Z A and ZB are the dynamic stiffness of the subsystem A and B. The other variables segment the
DoFs and Boolean matrices (B) for bookkeeping and implicit compatibility on the displacement degrees of
freedom u and force equilibrium for the external forces applied to system A (f A) using Lagrange Multipliers
λ A.
Isolating u A and u B from the first two lines in 1 and substitution in the third line yields an expression for
the interface forces λafter which one finds the responses of the assembled system as

2.2

Virtual Point Transformation

The Virtual Point Transformation ( 2) is a method to create test-based models from impact or shaker
measurements on a structure. The main idea is to define a point on or near a physical interface of a
substructure that one wants to couple to its neighboring (experimental or numerical) substructures.
Typically the Virtual Point contains three translations and three rotations for a total of six DoF per
Virtual Point. Here the assumption is made that the physical region surrounding the Virtual Point will
only move using the defined degrees of freedom, which is typically valid into the kHz range for test
equipment placed within a few centimeters of the Virtual Point.
Consider a tri-axial accelerometer that will measure responses in three perpendicular directions:. The responses of this accelerometer can be related to the responses at the virtual point ( q)bywhere here the q vector contains three translations and three rotations, and the transformation
matrix is generated using the distances between the sensor and the Virtual Point (rx,ry ,rz ) todetermine the rotations. Within Equation 4, we see that the accelerometer responses (u) are comprisedof not only the VP responses (q) related to rigid motion, but also some residual terms (μ).
While Equation 4 shows the relationship between measured and VP responses for a single
accelerometer, additional rows will be included for all k accelerometers around the Virtual Point.
Rewriting Equation 4 in terms of vectors gives the first part of Equation 5 below. Here, we want tosolve for the q Virtual Point responses that would best represent the actual responses (without any
residual terms). This is achieved with a pseudo-inverse of the Interface Displacement Mode (IDM)
matrix Ru , taking care to ensure we have an overdetermined matrix with nu (measured) > q (virtual)
DoF. A similar relation is written for the forces in Equation 6, this ti me using the IDM matrix of theforces (Ru ) to relate the physical forces f to the virtual forces m.

Using Equations 5 and 6, one can transform measured displacements (or accelerations) and forces,
respectively. Applied on FRF matrix level u = Yf one finds after substitution:

where Yqm is Virtual Point transformed matrix, usable as a test-based model in Dynamic
Substructuring.

Test-based

Simulation

modelsmodelsSystem model+(a)Dynamic+

Substructuring

Virtual NVH
with Component TPA

Source description
with Blocked Forces

(b)

(c)

Figure 1: (a) 3D scan of electric drive train with compressor connection in DIRAC measurement
software. Virtual points for coupling are shown as orange spheres. (b) Artificial airborne sound sourcein the reference vehicle engine compartment. (c) Schematic workflow for optimizing the compressor
isolation concept.
The compressor isolation concept is shown schematically in figure 1. The compressor is connected
to a bracket, which is connected to the vehicle’s electric drive train via three pressed-in rubberbushings. The modeling method with the best compromise between accuracy and effort is selected for

Design optimization

2.3 Industrial Case
This section discusses a substructuring example of an E-Compressor on a vehicle.

the individual components. The compressor can be modeled as a rigid body due to its modal properties.
FE modeling is selected for the bracket, which was done within COMSO L Multiphysics. The rubber
bearings are still to be designed. They are described with simple parametric models, where axial andradial directions have different stiffnesses. Their geometric alignment is part of the parameterization.
An experimental model of a similar reference vehicle is used for the complex transm ission path fromthe electric drive train to the driver’s ear, since neither a prototype nor a numerical model of the
project vehicle was available at this early stage. For this purpose, a 3D scan was created of the electric
drive train. The geometry is imported in the DIRAC measurement software in order to place
acceleration sensors, excitation points, and Virtual Points. The experimenta l vehicle model is createdin DIRAC and checked for physical plausibility (see Figure 1(a)). All component models wer e coupledthrough substructuring to simulate the transmission matrix from the compressor to the driver’s ear.
The Blocked Forces of the compressor are now required to describe the E -Compressor’s excitation.
Two compressors were compared with one another: the project compressor and a series compressor
that is already established on the market. For this purpose, they were freely suspended in an acoustic
test bench and equipped with acceleration sensors, and then a controlled run-up was measured. The
Blocked Forces of both compressors were determined inversely from their transfer function andoperational vibrations.
Figure 2(a) shows the norm of the translational Blocked Forces of project and series compressor
during run-up. The project compressor introduces an approx. 2 dB higher structure-borne soundexcitation into the system. Figure 2(b) shows the individual translational components of the Blocked
Forces of the project compressor (order filtered to the first order). It becomes clear that the twotranslational forces in the radial direction of the compressor, x and y, dominate) the overall excitation.

(a)

(b)

Figure 2: (a) Comparison of blocked forces for the project and production compressor, (b) Orderfiltered blocked forces for the project compressor
The operating forces increase approximately quadratically with the speed, which is typical for a n
unbalance excitation. This suggests using an imbalance value in [g x mm], calculated from the Blocked
Forces, as a component target.
The sound pressure in the interior can be predicted by equation 3 where the transmission matrix ofthe system full vehicle is simulated via substructuring. In this way, a virtual optimization can be
carried out on the system. This workflow is shown in Figure 1(c). In Figure 3, the sound level in thedriver’s cabin for the initially planned isolation concept is shown in red and the noise target level of
38 dB(A) in gray. The initial concept would have exceeded the target by 15 to 20 dB(A). The
problematic speeds are caused by acoustic interior modes of the reference vehicle and / or resonancesof the isolation concept. A parameter study showed that slight changes to the concept, such a s
additional masses or slightly modified bushing stiffness, do not provide sufficient leverage to meetthe interior noise goals. A significant change in the bearing stiffness and topology was necessary. The
operational deflection shapes of the compressor show that it is possible to develop an isolation conceptthat absorbs the inertia forces of the compressor, such as by road excitation, with stiffer axial bearing
directions. At the same time, the dominant imbalance operating vibrations of the compressor are
decoupled from the vehicle by soft radial bearing directions. The interior noise leve l for the optimized
isolation concept is shown in Figure 3 in green. With the optimized concept, the interior goals coul dbe achieved without any additional decoupling levels or masses

Figure 3: Prediction for structure-borne noise of initial and optimized isolation concept

3. Conclusion
More precise predictions are made in the early project phases by means of test -based models anddynamic substructuring. Using the Virtual Point Transformation technique allow accurate models thatallow decision-making in projects with target values at the driver’s ear directly. The industrial example
shows how, in an earlier phase than usual, the design concept could be verified and improved tocircumvent acoustic problems in a later stage.”

ACKNOWLEDGEMENTS
The authors would like to acknowledge VIBES.technology, Müller-BBM VibroAkustik System,
Magna and IPETRONIC for their support in this work.

REFERENCES[1] D. de Klerk, D. Rixen, and S. Voormeeren, “A General Framework for Dynamic Substructuring. History,
review and classifcation of techniques,” AIAA Journal, 2008.
[2] M. V. van der Seijs, Experimental Dynamic Substructuring, Analysis and Design Strategies for Vehicle
Development. Phd thesis, Delft University of Technology, 2016