MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSINGA METHOD FOR ORTHOGONAL AMPLITUDE AND DELAY PROCESSING
OF SUBJECTIVE LISTENING TEST MATERIAL
Aki Mäkivirta, Jan Abildgaard Pedersena
Genelec OY
Olvitie 5, 74100 Iisalmi, Finland
Tel: +358 17 813311, Fax: +358 17 812267
aki.makivirta@genelec.com(a) Bang & Olufsen a/s
DK-7600 Struer, Denmark
Tel: +45 96 84 48 97, Fax: +45 97 84 12 50
jgp@bang-olufsen.dk
Abstract – We present a method to change amplitude and delay responses in subjective listening test
material independently of each other. This is necessary in subjective listening experiments to apply
modern statistical methods treating simultaneously several statistical variables. A case study of producing audio test material with this method is presented. This is related to an experiment where theaudibility of the amplitude response variation and the delay response variation are studied at low frequencies based on data obtained from impulse responses of a room.

0. INTRODUCTION
Experimental designs based on using orthogonal arrays change more than one variable simultaneouslywith the aim to effectively determine the importance of several variables with a single test run. Orthogonal arrays were invented by Jacques Hadamar in 1897 and first used for statistical experimental
design by Plackett and Burman [1]. The motivation is to minimise the size of an experiment, to control
the amount of information required to be evaluated and to minimise the time and cost to execute anexperiment. Examples of statistical techniques using this approach include various factorial designs
such as Latin square type designs, balanced incomplete block designs, response surface methods andTaguchi techniques [1,2,3]. In this work we report the methodology for producing listening test material for an experiment related to orthogonal application of amplitude and phase deviations.
A room impulse response defines the transfer function H n(e jω ) from a loudspeaker location to a listening point. This transfer function, later called a kernel filter, typically does not have a flat amplitude
response or a constant group delay,mn (e jω ) = H n (e jω )grd n (e jω ) = −[]∂ arg H n (e jω ) .
∂ω(1)In our case, the response surface method [2,4] is applied to study the audibility of amplitude and delay
variation at low frequencies, below 200Hz [5,6]. The source data are simulated room impulse responses of a fixed size room for three different reverberation times, and additionally the anechoic case.

AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-25

1MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSING

1. ORTHOGONAL CONVOLUTION FILTERS
Testing the audibility of amplitude and delay the orthogonal experimental design exhaustively combines amplitude and group delay properties of room impulse responses to produce a set of filters representing their desired combinations. One way to achieve this is to design two filters. Filter Mn is responsible only for the amplitude response variation and has linear phase. Filter Gk is responsible only
for the delay variation and has allpass characteristic. The desired combination of the amplitude andphase characteristics is then produced as a convolution of these two filters. The resulting orthogonal
convolution filters

H nk = H ( mn , grd k ) = M n Gk ,n, k = { 1, 2, 3, 4,... }(2)

are then used to produce the listening test items.

2. AMPLITUDE PROPERTY
The object is to produce a filter M n (e jω ) having the amplitude behaviour of the kernel filter

H n (e jω ) at frequencies ω < ω o , H (e jω ) ,M n (e jω ) =  kc,

and a linear phase property(grd M n (e jω )) = d,

ω < ωoω > ωo(3)0<ω <π .

(4)

The desired magnitude response given by Equation 3 is interpolated onto a dense, evenly spaced grid.
A symmetric set of filter coefficients is obtained by applying an inverse fast Fourier transform to thegrid and multiplying by a Hamming window, resulting in a linear phase FIR filter having a constantdelay d.
In practice it is necessary to design the different filters Mn such that the constant gain levels c are thesame for frequencies ω > ω o for all filters to maintain right gain relationships for frequenciesω < ω o and avoid false cues after the processed listening test signals have been level aligned at
ω > ω o . The linear phase design of the amplitude property filter has a constant delay, which will add
the total delay of the final convolution filter.
Although we use the amplitude response characteristics of the kernel filter below a certain frequency(lowpass formulation), bandpass or highpass formulations of the amplitude response property are
equally possible.

3. GROUP DELAY PROPERTY
The object is to produce a filter H (e jω ) having delay variation of the kernel filter H n (e jω ) at frequencies ω < ω o ,[]grd H n (e jω ) + d 0 ,grd H (e jω ) = d1 ,[]ω < ωoω > ωo(5)0<ω <π .

(6)

and allpass amplitude characteristic

H (e jω ) = 1 ,AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-25

2MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSING

To obtain this filter, we use a method where a lowpass filter H LP (z ) , having a delay N, selects part of
the kernel filter response into H t (z ) .

H t ( z ) = H ( z ) ⋅ H LP ( z ) +(z−N− H LP ( z )) .

(7)

This filter has the desired delay variation characteristics but it does not have allpass characteristic. If
the amplitude response of H t (e jω ) does not contain zeros, we can design a whitening filter H i (z ) ,1
Gk ( z ) = H t ( z ) ⋅  = H t ( z) ⋅ H i ( z) H t ( z ) (8)such that

Gk (e jω ) = 1 ,0 <ω <π .

(9)This whitening filter is designed using the method described for obtaining the amplitude response
property, and it has linear phase.
We used FIR approximations that were forced causal by allowing enough constant delay d0 to modelthe delay variation required. In this way, this method can model the delay variation within the selected
frequency band, but the absolute delay of the room impulse response can not be modelled.
If in a listening test the delay property is switched in and out, it is necessary to compensate for theconstant delay term d1 to avoid the listeners from being mislead by the additional cue of the time shift
created by this constant delay.
Although above we use the delay characteristics of the kernel filter below a certain frequency (lowpassformulation), bandpass or highpass formulations of the delay property are equally possible.

4. CASE STUDY
Our case study is an experiment [5,6] where the target it to investigate the importance of the amplitude
and the delay variation, or ripple, at low frequencies. As the amplitude and delay ripple may also interact, the experimental design formulation exploiting orthogonal arrays is interesting because it allows us to study these interactions. The down side is that the preparation of listening test material iscomplicated by the requirement to dissociate the amplitude variation from the delay variation.
Room impulse responses used as the source data originate from simulation of an IEC 268-13 compliant room. The shape of the room is maintained in the simulation and the reflection coefficient of roomboundaries is used to vary the reverberation time of the room. Four values for reverberation time areused, the anechoic case and reverberation times RT=200ms, 400ms and 800ms [5]. This results in four
impulse responses (Fig. 1), each with their natural amplitude and delay variation. The frequency response of the radiating loudspeaker is eliminated by deconvolution with the anechoic impulse response. The anechoic response represents the properties of the radiating loudspeaker.
The resulting impulse responses show significant frequency dependent changes both in amplitude(Fig. 2) and delay (Fig. 3). The peak-to-peak amplitude variation in frequencies below 200Hz varies
from 15dB (RT=200ms) to 35dB (RT=800ms) and we can recognise the characteristic peaks andnotches of room amplitude response measurements. We also see the variations in delay typical to aroom at these extremes.

AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-253

MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSING

50
0-50
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5
time [s]

0.6

0.7

0.8

0.9

150
0-50
50
0-50
50
0-50Fig. 1. Room impulse responses simulated by varying the absorbance of room surfaces, from top tobottom: anechoic condition (reverberation time 0ms), 200, 400 and 800ms.
10RT=200ms
RT=400ms
RT=800ms

5Amplitude gain [dB]0-5-10-15-20-25-30
20406080100120Frequency [Hz]140160180200Fig. 2. Amplitude changes in the simulated room impulse responses.

AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-254

MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSING

RT=200ms
RT=400ms
RT=800ms

0.25
0.20.15

Group delay [s]

0.1
0.05
0-0.05-0.1-0.15
-0.2
-0.25

20406080

100120Frequency [Hz]140160180200Fig. 3. Delay variation in the simulated room impulse responses.

Amplitude property
The amplitude property filter (Fig .4) is implemented as a linear phase FIR filter. The amplitude in theimpulse responses is conditioned by removing frequencies <5Hz, essentially the DC component. The
subjective effect is limited below a corner frequency fc of either 80Hz or 120Hz by removing the amplitude ripple above these frequencies. The removal is implemented by modifying the filter design target. A filter is designed for each RT and corner frequency fc, resulting in six filters (RT=200ms, 400ms
and 800ms, fc=80Hz and 120Hz).

Delay property
The filters to implement the delay property (Fig. 5) are designed by modifying the target function
above the corner frequency fc to have a constant delay. The design method produces a FIR filter withallpass characteristics. Note that the real time delay that makes the filters causal has not been removedin Fig. 5. For the case fc=80Hz the delay changes to a constant value between frequencies 70…100Hz,
and for the case fc=120Hz the delay changes to a constant value between frequencies 80…120Hz.

Orthogonal filters
The experimental design produces a full permutation set of amplitudes and ripples. A total of 32 filters
are produced for this experimental design. Fig. 6 depicts some examples of the resulting FIR filters,
which are then convolved with the audio test material to produce the listening test items.
Typical modelling errors are depicted in Fig. 7 for the convolution filters in Fig. 6. The lower cornerfrequency for the modelling is 20Hz. The higher corner frequency for modelling is either 80Hz or120Hz. The modelling error is controlled between these frequencies. Above the higher corner frequency the modelling error becomes very large because the amplitude and delay assume constant values at these frequencies.

AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-25

5MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSING

10
RT=200m s
RT=400m s
RT=800m s

5A m plitude gain [dB ]0-5-10-15-20-25-30
20406080100120Frequency [Hz]140160180200

10RT=200m s
RT=400m s
RT=800m s

5A m plitude gain [dB ]0-5-10-15-20-25-3020406080100120Frequency [Hz]140160180200Fig 4. Amplitude filters for fc=80Hz (top) and fc=120Hz (bottom).

AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-256MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSING

0.75
RT=200m s
RT=400m s
RT=800m s

0.70.65
0.6

Delay [s]0.55
0.50.450.4
0.35
0.30.25
20406080

100120Frequency [Hz]1401601802000.75
RT=200m s
RT=400m s
RT=800m s

0.7
0.650.6

Delay [s]

0.55
0.5
0.45
0.4
0.35
0.3
0.25
20406080100120
Frequency [Hz]140160180200Fig. 5. Delay filters for fc=80Hz (top) and fc=120Hz (bottom).

AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-257MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSING

0.03
E X2RUN4AT80

0.02

Value

0.01

0-0.01

-0.02

-0.03
00.2

0.4

0.6

0.8

1Time [s]

1.2

1.4

1.6

1.8

20.06
E X2RUN2AT80
0.04

0.02

Value0-0.02

-0.04

-0.06

-0.08
00.2

0.4

0.6

0.8

1Time [s]

1.2

1.4

1.6

1.8

2

0.07
E X2RUN15AT80
0.06

0.05

Value

0.04

0.03

0.02

0.01

0-0.01
00.2

0.4

0.6

0.8

1Time [s]

1.2

1.4

1.6

1.8

2

Fig. 6. An example of convolution FIR impulse responses of room impulse response RT=800ms,
fc=80Hz. Both amplitude and phase (top), allpass or only delay (middle), linear phase or only amplitude (bottom).

AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-258MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSING

20room 3
1510

Gain error [dB]50-5-10-15-20-25-30
2030

4050

60

70

80

0.1
room 30.08
0.06

Delay error [s]

0.04
0.02
0-0.02
-0.04
-0.06
-0.08
-0.1
2030

4050Frequency [Hz]607080

Fig 7. Typical amplitude modelling error (top) and delay modelling error (bottom).

Convolution processing
The orthogonal filters are synthesised at the sampling frequency of 4410Hz, 1/10 of the audio sampling frequency for the listening test items. The convolution process is depicted in Fig. 8. The audio
material is crossover filtered at 150Hz by Hxo(z). This crossover filter is a 12th order maximally flatzero-phase implementation. The roll-off speed is fairly fast, and the lowpass section has 100dB attenuation at 400Hz. The attenuation is sufficient to remove aliasing in the decimation process. Zerophase implementation is possible because the audio material is processed off-line in a computer, allowing convenient time-inversion.
The lower band is decimated by 10 to make the convolution processing more efficient, then interpolated, filtered and added with the delayed and level aligned high frequency band to reconstruct thefull-bandwidth processed audio material. The anti-imaging filter Hr(z) is needed as a part of the reconstruction process for removing the images of the fundamental frequency band generated by the interpolation process. The convolution is implemented off-line in a PC computer, and all signal processing
is done in 64-bit floating point representation, but some intermediate storing is done in 16-bit PCM
format. The conversion to 16-bit PCM is done with dithering before truncation to minimise any distortion effects.
AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-25

9MÄKIVIRTA AND PEDERSEN

ORTHOGONAL AMPLITUDE AND DELAY PROCESSINGz-NG

HXO(z)+10Hnk(z)10Hr(z)Fig. 8. Block diagram of the convolution process.

5. DISCUSSION
Listening test techniques try to identify not only the primary influences but also their possible interactions. Modern statistical techniques based on orthogonal arrays provide a method of achieving thisgoal. We have presented a method to apply these techniques to studying ripple in amplitude and delay.
The amplitude and delay ripples are modelled separately as FIR filters. While FIR filters may not becomputationally the most effective they are flexible and easy to design and provide the additional advantage of a precisely linear phase.
Multirate processing makes the convolution feasible in a rational amount of time and computer power.
The disadvantage is that additional design steps are needed to align the highpass path with the lowpass
path both in level and phase. This is made easier in our implementation by constraining the orthogonal
filters to have a flat amplitude response and a constant integer delay at frequencies near the crossover.

6. ACKNOWLEDGEMENTS
This work is a part of the Eureka project EU1653 Medusa (Multichannel Enhancement of Domestic
User Stereo Applications). The Medusa project is a 3.5-year joint research project of the following
parties: Bang & Olufsen, British Broadcasting Corporation, Genelec, Institute of Sound Recording at
the University of Surrey, and Nokia Research Center. The aim of this project is to examine the variables of the domestic multi-channel system, with and without picture, to carry out the essential optimisation leading to consumer end-products.

7. REFERENCES
1.
2.
3.

4.
5.

6.

Phillip Ross: "Taguchi Techniques for Quality Engineering: Loss Functions, Orthogonal Experiments, Parameter and Tolerance Design", McGraw-Hill, New York, 1988.
George E. P. Box, William G. Hunter, J. Stuart Hunter: "Statistics for Experimenters", John
Wiley & Sons, New York, 1988.
G. Taguchi, Y. Yokoyama: "Taguchi Methods: Design of Experiments", American Supplier Institute, Dearborn MI, in conjunction with the Japanese Standards Association, Tokyo, Japan,
1994.
G. E. P. Box, N. R. Draper: "Empirical Model-Building and Response Surfaces", Wiley & Sons,
New York, 1987.
Jan Abildgaard Pedersen and Aki Mäkivirta: "Quantification of Subwoofer Requirements, Part I:
Generation of Stimuli and Listening System Equalization", AES 108th Convention, Paris 19-22Feb, 2000.
Søren Bech: "Quantification of Subwoofer Requirements, Part II: The influence of Lower System
Cut-off Frequency and Slope, and Pass-band Amplitude and Group Delay Ripple", AES 109thConvention, Los Angeles 22-25 Sep, 2000.

AES 109th CONVENTION, LOS ANGELES, 2000 SEPTEMBER 22-2510