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Title

Study on method of estimating direction ofarrival using monaural modulation spectrum

Author(s)Ando, Masaru; Morikawa, Daisuke; Unoki, Masashi

Citation

Journal of Signal Processing, 18(4): 197‑200

Issue Date

2014

Type

Journal Article

Text version

publisher

URL

http://hdl.handle.net/10119/12893

RightsCopyright (C) 2014 信号処理学会. Masaru Ando,
Daisuke Morikawa, and Masashi Unoki, Journal of
Signal Processing, 18(4), 2014, 197‑200.
http://dx.doi.org/10.2299/jsp.18.197

Description

Japan Advanced Institute of Science and Technology

Journal of Signal Processing, Vol.18, No.4, pp.197-200, July 2014

SELECTED PAPER AT NCSP'14

Study on Method of Estimating Direction of Arrival Using Monaural Modulation Spectrum
Masaru Ando, Daisuke Morikawa and Masashi Unoki
School of Information Science, Japan Advanced Institute of Science and Technology
1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
E-mail:{ma ando, morikawa, unoki}@jaist.ac.jp

Abstract
Human beings can localize a target sound by using binauralcues. On the other hand, we can also localize a target soundby using monaural cues. The monaural modulation spectrum (MMS) can be regarded as an important cue of monaural sound localization. A method of estimating direction ofarrival (DOA) using a machine learning scheme for classification of MMS patterns has been proposed. However, thismethod cannot account for the monaural DOA mechanism byusing MMS patterns. To further investigate how the MMS
plays an important role in monaural sound localization, we
aimed to find cues in the human ability for monaural sound localization and propose a method of estimating DOA by using
these cues. We investigated how the MMS of observed signals vary with the azimuth. As a result, shapes of the MMS
were drawn as arcs with azimuth variations. We then proposed a method of estimating monaural DOA using these results. Simulations were carried out to verify the effectivenessof the proposed method. We found that the proposed method
could estimate DOA using the MMS, except with front-backconfusion discrimination.
1. Introduction

(a)

(b)

Source signal

Transfer function���)���� �)Observed signal
���� �)���)���� �)���� �)��� ��)��� ��� �)��� ��� �)�� ��� )�� ��� � �)�� ��� � �)

Figure 1: Relationship between sound source signals and observed signals at eardrum position: (a) Time domain and (b)Power envelope domain
in the monaural spectral envelope vary with the DOA of thesound source; therefore, these cues cannot be used to directly
estimate the DOA of a sound source.
On the other hand, there have been studies on binauralmodulation cues for sound localization. Thompson and Dau
reported that ILD and ITD in the temporal envelope are also
important cues of sound localization [3]. This report suggests that the monaural modulation spectrum (MMS) can be
regarded as an important cue of monaural sound localization.
There have been related studies conducted regarding DOA
with the MMS approach. Kliper et al. proposed a DOA estimation method using monaural cues in amplitude modulation patterns based on a machine learning scheme [4]. They
used the MMS patterns of signals observed at the eardrum
position. However, they used the machine learning scheme
to classify the MMS patterns to directly estimate the azimuthof the sound source. Therefore, their method cannot accountfor the monaural DOA mechanism. In particular, with their
method, it is still unclear how the MMS patterns can be used
for monaural sound localization.
We aimed to find important monaural cues for sound localization and propose a method of estimating DOA using thesecues. We investigated how the MMS of the observed signals
vary with the azimuth to find monaural cues of DOA estimation. We propose a method based on the concept of themodulation transfer function (MTF).

Human beings have the ability of sound localization. For
example, we can easily localize the direction of an on-coming
car from the noise from the car. In general, human beings
use binaural cues to localize a target sound. It has been reported that humans can also localize a target sound by using
monaural cues [1]. Gaining knowledge on the human abilityof sound localization is important in learning more about ourhearing mechanism. A method of estimating the direction ofarrival (DOA) of a target sound using monaural cues can beapplied to single-channel signal processing if we can apply
our ability of sound localization to engineering problems.
The main cues for sound localization by using binauralhearing are interaural time difference (ITD), interaural level
difference (ILD), and spectral information [2]. They are included in the head-related transfer function (HRTF), which
is a transfer function between a sound source and eardrum
position in each ear. In these cues, available monaural cues
for sound localization can be regarded as spectral cues in the 2. Model Concept
HRTF such as peeks and notches in the monaural spectral envelope. However, it is unclear how the peeks and notches
Figure 1(a) shows a transfer function from the sound

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−70
Measured values
Regression curve

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(b) f = 20 Hz
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(c) fm = 200 Hz

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Modulation spectrum [dB]

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Modulation spectrum [dB]

Modulation spectrum [dB]

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(a) f = 2 Hz

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Modulation spectrum [dB]

Modulation spectrum [dB]

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(a) f = 2 Hzm

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Measured values
Regression curve

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Azimuth [deg.]

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(c) f = 200 Hz
m

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Figure 2: MMS characteristics with varying azimuth by AM Figure 3: MMS characteristics with varying azimuth by AM
signalnoise
Equation (3) can be represented in the modulationsource to the observed signal at the eardrum position in thetime domain, where y(t, θ), h(t, θ), x(t), and θ are the ob- frequency domain asserved signal, head-related impulse response (HRIR), soundEy (fm , θ) = Eh (fm , θ)Ex (fm )(4)source signal, and arrival direction of the sound source signal,
respectively. The observed signal is represented aswhere Ey (fm , θ), Eh (fm , θ), and Ex (fm ) are MMS ofy(t, θ), head-related MTF (HRMTF), and MMS of x(t), rey(t, θ) = h(t, θ) ∗ x(t)(1) spectively. The term fm is the modulation frequency. Then,
HRMTF is defined aswhere ∗ is a convolution operation. The HRIR includes
 ∞acoustic characteristics such as pinna reflection and heade2h (t, θ)exp(−j2πfm t)dt
(5)
Eh (fm , θ) =diffraction.
0
Equation (1) can be represented in the frequency domain
In this study, e2y (t, θ) was extracted byas
Y (f, θ) = H(f, θ)X(f )(2)(6)
e2y (t, θ) = LPF |y(t, θ) + jHilbert[y(t, θ)]|2
where Y (f, θ), H(f, θ), and X(f ) are the spectrum of theobserved signal, HRTF, and spectrum of sound source signal, where LPF[·] is a low-pass filtering and Hilbert[·] is therespectively. Figure 1(b) represents a transfer function in the Hilbert transform. This equation is based on calculation ofmodulation domain from the power envelope of the original the instantaneous amplitude, and low-pass filtering is used tosignal to that of the observed signal. This function is in a remove the higher modulation-frequency components in the
different domain, as shown in Fig. 1(a), which is based on power envelope as post-processing. We use the LPF with athe concept of the MTF [5], [6]. The power envelope of the cut-off frequency of 200 Hz. Finally, e2y (t, θ) is transformed
observed signal e2y (t, θ) can be represented as
to Ey (fm , θ) using fast Fourier transform (FFT).
e2y (t, θ) = e2h (t, θ) ∗ e2x (t)(3) 3. Monaural Modulation-Spectrum Analysis

where e2h (t, θ) and e2x (t) are the power envelopes of h(t, θ)
We investigated how the MMSs of the observed signals
and x(t).
vary with varying azimuth; from 180 to 355 degrees, in which

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Journal of Signal Processing, Vol. 18, No. 4, July 2014

(a) Training phase���� �)���� �)Power envelope
calculation(Eq.(6))

�� ��� � �)

FFTRegression
coefficient
calculation(Eq.(7))� � ��� � ���� ��� )Parameter tables�� � ����� � �� � ���� � ����� � �� � ��⋮�� � ������� � �� � ���� � �� � ��(b) Estimating phase��� ��� �)

��

���)

���)

Power envelope
calculation(Eq.(6))

��� ��)FFT�� ��� )Figure 4: Proposed method: (a) Training phase and (b) Estimating phasethe front of the head was at 0 degrees, through computer simulations. In these simulations, the observed signals were generated by convoluting the sound source signal with HRIRs.
The analysis range of the azimuth corresponded to the left
ear side. We used the HRTF database, which was recordedby the Research Institute of Electrical Communication of Tohoku University. The HRIRs of 114 people (228 ears) wererecorded in this database. The recoding positions were 1225
points. The azimuth interval was 5 degrees and the elevation interval was 10 degrees. The sampling frequency was
48 kHz. In our simulations, HRIRs containing ham noise andlarge differences between neighboring angles at the lower frequency components were eliminated from all conditions.
Two types of the amplitude modulated (AM) signals wereused in these simulations as the sound source. One was an
AM signal with a sinusoidal carrier of 10 kHz (AM signal)and the other was an AM signal with a white noise carrier(AM noise). Three modulation frequencies, 2, 20, and 200
Hz, were used in these signals. Simulations were carried out
to investigate the relationships between MMSs and the observed signals with azimuth.
Figures 2 and 3 show the simulation results for observed
AM signal and AM noise. The horizontal axis indicates theazimuths of the observed signals and the vertical axis indicates the MMS values. We found that the shapes of the
MMS varied with azimuth and formed an arc as a function of
the azimuth. These shapes were not symmetrical at 270 degrees, i.e., at the left ear side. These characteristics could beobserved under all the modulation frequencies and types ofstimuli. The MMS shapes with the AM noise were smootherthan those with the AM signal. This trend varied dependingon the individual’s ears. Similar trends could be also observed
for the right ears the left ear. The dynamic ranges of MMS
variations were almost the same with all modulation frequencies, as shown in Figs. 2 and 3. Although we omit theseresults in this paper, similar trends could be observed in thesimulations by using the other HRIRs. Therefore, we argue
that this effect is cause by HRIR personality.
These results suggest that humans may use cues based on

Journal of Signal Processing, Vol. 18, No. 4, July 2014

Direction
estimation(Eq.(8))��

the tendency of variation in the MMS. However, it is necessary to carry out a listening experiment.
4. Proposed Method
We propose a method of estimating DOA based on the results of MMS analysis. The flow of the proposed method isshown in Fig. 4. The MMS values are plotted with open circles in Figs. 2 and 3. These plots are approximated using
second order polynomials as follows:Eˆy (fm , θ) = p1 (fm )θ2 + p2 (fm )θ + p3 (fm )(7)where p1 (fm ), p2 (fm ), and p3 (fm ) are the regression coefficients and Eˆy (fm , θ) is the approximated value. The solidlines in Figs. 2 and 3 indicate the ideal results from Eq.
(7). An inverse function is derived by using these regression
curves. This can be represented as follows:−p2 ± p22 − 4p1 (p3 − Ey )θ̂(Ey ) =(8)
2p1
where θ̂ is the estimated azimuth. If HRIR is known, p1 ,p2 , and p3 can be calculated from the MMS of the observed
signals y(t, θ).
We assume that the input signal of the proposed method
is y(t) with unknown azimuth θ. Then, the power envelopee2y (t) is calculated using Eq. (6) and Ey (fm ) is calculatedusing the FFT. Finally, the unknown azimuth θ is estimatedby substituting the MMS values and regression coefficients
into Eq. (8).
5. Evaluations
Simulations were carried out to verify the effectiveness ofthe proposed method. The AM signal, AM noise, and left ear
side were used in these simulations. Figure 5 shows the simulation results. The horizontal axis indicates the azimuths of
the input signals and the vertical axis indicates the estimated

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(a) fm = 2 Hz

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Estimated angle [deg.]

azimuths. There was no effect by varying the modulation frequency, as shown in Fig. 5.
Two azimuths were estimated as positive and negative values derived by the inverse function of Eq. (8). For the positive value, estimates were correct in the back of ear position
while, estimates were correct in the front of ear position for
the negative value. However, in each reverse , estimates wereincorrect. These false estimates were due to front-back confusion. Moreover, there were more false estimates with theAM signal than with AM noise.
These results indicate that the proposed method can correctly estimate DOA using the MMS, except with front-backconfusion discrimination.
6. Conclusions

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+ AM noise− AM noise+ AM signal− AM signal
Ideal estimation

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Acknowledgments
This work was supported by the Strategic Information andCommunications R & D Promotion Programme (SCOPE:
131205001) of the Ministry of Internal Affairs and Communications (MIC), Japan. It was also supported by a Grant-in-Aid
for Young Scientists (Start-up, No. 25880011).

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(b) f = 20 Hz

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We investigated how the MMS of observed signals varywith the azimuth. The results showed that the MMS variedwith the azimuth where the peak of the shape was around theear position. We then proposed a method of estimating DOA
based on our analysis results. These results indicated thatthe proposed method could correctly estimate DOA using the
MMS, except with front-back confusion discrimination.
For future work, we will investigate how to solve the discrimination problem with regard to front-back confusion.

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References

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