Acoust. Sci. & Tech. 25, 2 (2004)

PAPER

Evaluation of separation and dereverberation performancein frequency domain blind source separation
Ryo Mukai, Shoko Araki, Hiroshi Sawada and Shoji Makino
NTT Communication Science Laboratories, NTT Corporation,
2–4 Hikaridai, Seika-cho, Soraku-gun, Kyoto, 619–0237 Japan( Received 12 November 2002, Accepted for publication 20 August 2003 )Abstract: In this paper, we propose a new method for evaluating the separation and dereverberation
performance of a convolutive blind source separation (BSS) system, and investigate a separating
system obtained by employing frequency domain BSS based on independent component analysis(ICA). As a result, we reveal the acoustical characteristics of the frequency domain BSS for
convolutive mixture of speech signals. We show that the separating system removes the direct soundof a jammer signal even when the frame length is relatively short, and it also reduces the reverberationof the jammer according to the frame length. We also conﬁrm that the reverberation of the target is not
reduced. Moreover, we propose a technique, suggested by the experimental results, for improving thequality of the separated signals by removing pre-echo noise.
Keywords: Blind source separation, Independent component analysis, Frequency domain, Convolutive mixtures, Impulse response, Performance evaluation.
PACS number: 43.60.Gk, 43.60.Cg, 43.60.Qv

1.

INTRODUCTION

Blind source separation (BSS) is a technique for
estimating original source signals using only observed
mixtures of signals. The BSS of audio signals has a wide
range of applications including noise robust speech
recognition, hands-free telecommunication systems andhigh-quality hearing aid equipment.
Independent component analysis (ICA) is a typical BSS
method that is eﬀective for instantaneous (non-convolutive) mixtures [1–3], and many attempts have been made toapply BSS to signals mixed in convolutive environments[4–8]. However, it has also been pointed out that an
adequate performance level cannot be obtained in environments with long reverberation where the ﬁlter lengths ofthe mixing and separating systems are of the order of
thousands or higher [9–11].
Although there have been a large number of studies of
BSS, little attention has been paid to the physical andacoustical characteristics of the separating system, since
ICA was originally a statistical method. It is useful toinvestigate the acoustical nature of BSS with a view toimproving separation performance, and some researchers
have begun to investigate and utilize its physical properties.
e-mail: ryo@cslab.kecl.ntt.co.jp[DOI: 10.1250/ast.25.119]

The eﬀect of early reﬂection and reverberation on BSS isinvestigated in [12]. The relationship between BSS andbeamformers is utilized to achieve a better performance in[13,14]. Still only a few physical characteristics is known.
In this paper, we propose a method for analyzing aseparating system obtained by frequency domain BSS for
convolutive mixture of speech signals from an acoustical
viewpoint. We measure the impulse responses of straightand cross paths of the separating system, and examine theseparation performance in detail. We focus our attention on
the power of (1) the direct sound of the target signal, (2) thereverberation of the target signal, (3) the direct sound of thejammer signal, and (4) the reverberation of the jammer
signal, and evaluate each power separately.
As a result, we reveal the acoustical characteristics offrequency domain BSS based on ICA. We show that the
separating system removes the direct sound of the jammer
signal even when the frame length is relatively short, and it
also reduces the reverberation of the jammer according to
the frame length. We also conﬁrm that the reverberation of
the target is not reduced as expected. Moreover, we
propose a technique, suggested by the experimental results,
for improving the quality of the separated signals by
removing pre-echo noise.
The inability to achieve target dereverberation can bepredicted and explained by the ambiguity of a linear

119

Acoust. Sci. & Tech. 25, 2 (2004)

transformation of BSS [15,16]. However other characteristics were unknown until we revealed them by means ofexperiments. Our results also provided experimental conﬁrmation of the equivalence between BSS and adaptive
beamformers (ABF) which is discussed in [17,18].
The paper is organized as follows. In the next section,
we summarize the algorithm of frequency domain BSS for
convolutive mixtures. In Section 3, we deﬁne performancemeasurement factors using impulse responses and theirpower. Section 4 presents experimental results obtainedusing speech signals. In Section 5, we discuss theacoustical characteristics of the BSS system obtained byfrequency domain ICA. Section 6 concludes this paper.

2.

BSS OF CONVOLUTIVE MIXTURES

2.1. Frequency Domain ICA
When the source signals are si ðtÞ ð1  i  NÞ, thesignals observed by microphone j are xj ðtÞ ð1  j  MÞ,and the separated signals are yk ðtÞ ð1  k  NÞ, the BSS
model can be described by the following equations:xj ðtÞ ¼

N
Xðhji  si ÞðtÞ

ð1Þ

i¼1

yk ðtÞ ¼

M
Xðwkj  xj ÞðtÞ

ð2Þ

j¼1

where hji is the impulse response from source i to
microphone j, wkj is the coeﬃcient when we assume thata separating system is used as FIR ﬁlters, and  denotes the
convolution operator.
A convolutive mixture in the time domain corresponds
to instantaneous mixtures in the frequency domain. Therefore, we can apply an ordinary ICA algorithm in thefrequency domain to solve a BSS problem in a reverberant
environment. Using a short-time discrete Fourier transformfor (1), the model is approximated as:Xð!; nÞ ¼ Hð!ÞSð!; nÞ;ð3Þ

where ! denotes the frequency, and n represents the frame
index. The separating process can be formulated in eachfrequency bin ! as:Yð!; nÞ ¼ Wð!ÞXð!; nÞ¼ Wð!ÞHð!ÞSð!; nÞ;ð4Þ

W iþ1 ¼ W i þ ½I  hðYÞY H iW i ;ð6Þ

where i is an index for the iteration, I is an identity matrix,
 is a step size parameter, hi denotes the averaging
operator, and ðÞ is a nonlinear function. Because thesignals are complex valued in the frequency domain, we
use a polar-coordinated based nonlinear function [20]:ðYÞ ¼ tanhðg  absðYÞÞe|argðYÞ ;ð7Þ

where g is a gain parameter to control the nonlinearity.
The above calculations are carried out separately foreach frequency.
2.2. Permutation and Scaling Problem
Once we have solved ICA for all frequencies, we needto solve the permutation and scaling problems. Since weare handling signals with complex values, the scaling
factors are also complex values. Thus the scaling can bedivided into phase scaling and amplitude scaling.
We use the method described in [13] to solve thepermutation and phase scaling problems. When we
consider a separating system as a microphone array, we
can write directivity patterns for every frequency bin. The
permutation problem is solved so that the null directions
are aligned. We can estimate the directions of the source
signals from the aligned directivity patterns, and the phasescaling problem is solved so that the phase response of theestimated source direction becomes zero.
The amplitude scaling problem is solved by the method
reported in [21] with a slight modiﬁcation. We calculate
the inverse of the separating matrices Wð!Þ1 , and decide
the scaling factors so that the norms of each column ofWð!Þ1 become uniform.
In the following sections, we consider a two-input, twooutput convolutive BSS problem, i.e., N ¼ M ¼ 2 (Fig. 1).

3.

EVALUATION METHOD

The BSS performance is usually evaluated by the signal
to interference ratio (SIR), which is deﬁned as the ratio of a

ð5Þ

where Sð!; nÞ ¼ ½S1 ð!; nÞ; . . . ; SN ð!; nÞT is the source
signal in frequency bin !, Xð!; nÞ ¼ ½X1 ð!; nÞ; . . . ;XM ð!; nÞT denotes the observed signals, Yð!; nÞ ¼
½Y1 ð!; nÞ; . . . ; YN ð!; nÞT is the estimated source signal,and Wð!Þ represents the separating matrix. Wð!Þ isdetermined so that Yi ð!; nÞ and Yj ð!; nÞ become mutuallyindependent (i 6¼ j).
To calculate the separating matrix W, we use an
optimization algorithm based on the minimization of the120

mutual information of Y. The optimal W is obtained by thefollowing iterative equation using the natural gradientapproach [19]:Fig. 1 Model of BSS system.

R. MUKAI et al.: PERFORMANCE EVALUATION OF FREQUENCY DOMAIN BSS

target-originated signal to a jammer-originated signal[9,10,22]. This measure is reasonable for evaluating theseparation performance, but unsuitable for evaluating the
dereverberation performance because of its inability to
distinguish the direct sound and reverberation. Since wewish to know the components of separated signals in detail,i.e., the direct sound and reverberation of the target andjammer, we adopt the following procedure.
(i) We estimate the separating matrix Wð!Þ for eachfrequency.
(ii) By using IFFT, we transform the frequency domain
separating matrix Wð!Þ to time domain separatingﬁlter wij ðtÞ.
(iii) We measure four impulse responses, from s1 to y1 , s1
to y2 , s2 to y1 , and s2 to y2 .
(iv) We investigate the four impulse responses in detailand compare them with the responses of a null
beamformer (NBF).
3.1. Deﬁnitions of Performance Measurement Factors
We evaluate the performance of the separating systemin the time domain. We consider a separated signal y1 ,target signal s1 , and jammer signal s2 . When the target s1 is
an impulse ðtÞ and the jammer s2 ¼ 0, we represent theobserved signal x1 as x1s1 [Fig. 2(a)], and y1 as y1s1 [Fig.
2(b)]. Similarly, when s1 ¼ 0 and s2 ¼ ðtÞ, we represent x1
as x1s2 , and y1 as y1s2 [Fig. 2(c)]. x1s1 is an impulse response
from s1 to x1 caused by the mixing system H, and y1s1 is an
impulse response from s1 to y1 caused by the whole system
W  H. These values are calculated by using hij and wij asfollows.
x1s1 ¼ h11

ð8Þ

x1s2 ¼ h12

ð9Þ

y1s1 ¼ w11  h11 þ w12  h21

ð10Þ

y1s2 ¼ w11  h12 þ w12  h22

ð11Þ

In terms of source separation, we can consider y1s1 to be thedirect and reverberant sound of target s1 , and y1s2 to be theremaining sound of jammer s2 .
To simplify the evaluation, we normalize hji so that thepower of the observed signals x1s1 and x1s2 is equal to 0 dB,
and employ the following deﬁnitions.
. PI : the power of x1s1 . (normalized to 0 dB). PT : the power of y1s1 . (scaled to 0 dB). PJ : the power of y1s2 .
. PIR : the power of the reverberant sound in x1s1 ,. PTR : the power of the reverberant sound in y1s1 ,. PJR : the power of the reverberant sound in y1s2 .
These are calculated as follows:
PI ¼

1
X

jx1s1 ðtÞj2 ;

PIR ¼

t¼1

PT ¼

1
X

1
X

jx1s1 ðtÞj2

ð12Þ

t¼

jy1s1 ðtÞj2 ;

PTR ¼

t¼1

PJ ¼

1
X

1
X

jy1s1 ðtÞj2

ð13Þ

jy1s2 ðtÞj2

ð14Þ

t¼

jy1s2 ðtÞj2 ;

PJR ¼

t¼1

1
X
t¼

where  is an appropriate time between the arrival of thedirect sound and the reverberant sound, which is determined according to experimental conditions. Usually, theimpulse response in a real room consists of direct sound,early reﬂection and reverberation. There are a delay and alevel diﬀerence between the direct sound and the ﬁrst
reﬂection due to the diﬀerence between their paths. We
consider that the early reﬂections are included in thereverberation, thus  is set to the time just before the arrivalof the ﬁrst reﬂective sound. These measurement factors canbe indicated on the the power attenuation curves in Fig. 2
We also deﬁne the reduction ratio of the reverberationof target signal RT and the reduction ratio of jammer signal
RJ as follows
PTR
(dB)
PIR
PJ
RJ ¼ 10 log¼ 10 log PJ (dB):PT

RT ¼ 10 log

ð15Þ
ð16Þ

For the analysis of the residual jammer signal in thefollowing section, we also deﬁne the power of the earlypart of the residual jammer signal as follows:X
jy1s2 ðtÞj2
PJE ¼
1<t<

¼ PJ  PJR ;Fig. 2 Impulse responses of (a) observed target, (b)straight path and (c) cross path, and their power
attenuation curves.

ð17Þ

which is the total power of the remaining direct sound andthe non-causal noise called pre-echo.

121

Acoust. Sci. & Tech. 25, 2 (2004)

Fig. 3 Layout of the room used for the experiments.
Reverberation time Trev ¼ 300 ms.

4.

EXPERIMENTS

In order to examine what is separated by a separating
system based on ICA, and what remains as noise, weinvestigated the impulse responses of a system. In
frequency domain BSS, it has been conﬁrmed that the
separation performance changes according to the length of
the frame [10], therefore we chose the frame length as aparameter. In our experiment, the length of the ﬁlters of theseparating system was the same as the frame length.
4.1. Experimental Conditions
The layout of the room we used to measure the impulse
responses of the mixing system H is shown in Fig. 3. The
reverberation time of the room Trev was 300 ms, whichcorresponds to an impulse response of 2,400 taps at an
8 kHz sampling rate. We used a two-element array with aninter-element spacing of 4 cm, which corresponds to almost
the half-wave length of the Nyquist frequency 4 kHz. This
spacing makes it possible to avoid spatial aliasing over thewhole frequency range. The speech signals arrived fromtwo directions, i.e., 30 and 40 . The contribution of thedirect sound of h11 and h21 was 5.7 dB, and that of h12 andh22 was 6.6 dB.
We carried out experiments with 42 signal source
combinations using seven sentences spoken by two maleand two female speakers selected from the ASJ continuous
speech corpus. Each of these mixed speech signals were six
seconds long. We used the entire six seconds of the mixed
data for learning according to (6).
In these experiments, we changed the frame length Tfrom 4 to 8,192 and investigated the performance undereach condition. The sampling rate was 8 kHz, and theanalysis window was a Hanning window. The frame shift S
was T=4.
The step size parameter  aﬀects the convergence ofthe separating system W and the separation performance.
We varied  from 0.01 to 0.5, and selected the best step
size for each frame size T. We used  ¼ 0:1 for T  1,024,

122

Fig. 4 Target and jammer impulse responses of NBF
and ICA (T = 2,048, Trev ¼ 300 ms).

 ¼ 0:05 for T ¼ 2,048, and  ¼ 0:02 for T  4,096. The
gain parameter g is 1. This means that the nonlinear
function ðYÞ ¼ e|argðYÞ . The number of iterations for (6) is100.
4.2. Experimental Results
Figure 4(a) and (c) show examples of impulse
responses y1s1 and y1s2 of the separating system obtainedby a null beamformer (NBF) that forms a steep null
directivity pattern towards a jammer on the assumption thatthe jammer’s direction is known. Figure 4(b) and (d) areresults obtained by ICA.
For the target signal, we can see that the reverberation
passes the system in both cases (NBF and ICA) in Fig. 4(a)and (b). Figure 4(c) shows that the direct sound of thejammer is eliminated, but the reverberation is not eliminated by the NBF, as expected. By contrast, Fig. 4(d)indicates that ICA not only eliminates the direct sound, butalso reduces the reverberation of the jammer. However, we
can also observe the appearance of non-causal noise. We
discuss this in the following section.
Figure 5 shows the relationship between the frame
length T and the reduction ratios RT and RJ deﬁned by (15)and (16). Figure 5(a) shows results provided by ICA. For
the sake of comparison, the NBF performance is shown in
Fig. 5(b).
Note that these results are measured by using the powerof the impulse responses, and diﬀer from the noise
reduction rate (NRR) [10] measured by using a speech
signal with a highly colored spectrum. Our results indicate
larger values than the NRR.

R. MUKAI et al.: PERFORMANCE EVALUATION OF FREQUENCY DOMAIN BSS

Fig. 5 Relationship between frame length and reduction
ratios (Trev ¼ 300 ms). The target reduction ratio RT
and the jammer reduction ratio are deﬁned by (15) and(16).

Figure 6 shows the power of the residual jammer signal
PJ and its decomposition into the early part PJE and theresidual reverberation PJR . We used  ¼ 2 ms (16 taps).
Figure 6(a) is the result of ICA and Fig. 6(b) is the result of
NBF.

5.

DISCUSSION

5.1. Jammer Reduction and Target Dereverberation
First, we discuss the jammer reduction ratio RJ in Fig. 5.
When T  128, the reduction performance of BSS is as
poor as that of NBF, and when 256  T  2,048, thereduction ratio increases. When T ¼ 2,048, the average RJ
value is 16.7 dB. This is much greater than the contributionof the direct sound (6.6 dB). This means that the separating
system obtained by ICA can reduce not only the direct
sound of the jammer but also its reverberant sound.
However, as we describe later, the reverberation is not
eliminated completely.
By contrast, the reduction ratio of the reverberation oftarget RT is low, and does not vary throughout the entire
frame length T. This means that dereverberation was notachieved for the target signal. From these results, we canconclude that W is not the approximation of the inverse
system of H, but a ﬁlter that can eliminate the jammer
signal.
It has been pointed out that early reﬂections of thejammer signal are removed by BSS [12]. We obtained aslightly stronger result that not only the early reﬂections

Fig. 6 Analysis of the power of the residual jammer
signal (Trev ¼ 300 ms). PJ is the power of the residual
jammer signal, which is decomposed into the early part
PJE and the residual reverberation PJR .

but also the reverberation of the jammer signal is reduced
to some degree. The reason for this is that frequency
domain BSS works like two sets of frequency domain
adaptive microphone arrays, i.e., adaptive beamformers(ABF), which adapt to minimize the jammer signal
including reverberation. Figure 7 shows the directivity
patterns of NBF, the separating system obtained by ICA,
and ABF. ICA and ABF provide duller directivity thanNBF, thus they can remove not only the direct sound of thejammer but also its reverberation. A theoretical discussionof the relationship between frequency domain BSS using
second order statistics and ABF can be found in [17].
5.2. Analysis of Residual Jammer Signal
Next, we examine the power of the residual jammer
signal PJ in detail. Figure 6 shows the power of the residual
jammer signal PJ and its decomposition to PJR and PJE . PJR
is the contribution of the residual reverberation. PJE is thecontribution of the early part of the residual jammer signal,
which consists of the pre-echo noise and the residual direct
sound of the jammer signal.
Figure 8 shows the jammer impulse responses forvarious frame lengths. From Figs. 6 and 8, we can derivefollowing consideration.
When the frame length is too short, the direct soundcannot be removed by the separating system, and it123Acoust. Sci. & Tech. 25, 2 (2004)

Fig. 8 Jammer impulse responses of BSS system.

Fig. 7 Directivity patterns of (a) NBF, (b) separating
system obtained by ICA, and (c)ABF (T = 2,048,
Trev ¼ 300 ms).

degrades the separation performance. When 64  T 
1,024, the direct sound is removed well, however the ﬁlter
is much shorter than the length of the reverberation;accordingly, any reverberation that is longer than the ﬁlter
cannot be reduced at all.
As the frame length becomes longer, the number ofcoeﬃcients to be estimated increases while the number ofdata samples for learning in each frequency bin decreases,
since we are using ﬁnite length data of 6 seconds. For
example, when T ¼ 8,192 and S ¼ T=4, each frequency
bin has only 24 data samples and this is insuﬃcient for thestatistical estimation. As a result, the amount of estimation
errors increases.
Moreover, the pre-echo noise grows, and this causes
the performance to decline. Furthermore, the noise damages the target signal when T is too long (Fig. 9). Thus,
there is a tradeoﬀ between coverage of reverberation andestimation errors.

124

Fig. 9 Target impulse response of BSS system damagedby pre-echo noise.

5.3. Eliminating Pre-echo NoiseThe pre-echo noise is mainly caused by the estimation
errors in the non-causal part of the unmixing ﬁlters.
Therefore, if we allow a delay in proportion to the frame
length (half of the frame length in the above experiments),
the noise increases as the frame length become longer. The
pre-echo noise can be removed by eliminating the noncausal part of the separating ﬁlters. However, this prevents
the separating system from removing the direct sound of
the jammer signal (Fig. 10), and degrades the separation
performance.
One solution is to limit the non-causal part of theseparating ﬁlters to an appropriate length instead of

R. MUKAI et al.: PERFORMANCE EVALUATION OF FREQUENCY DOMAIN BSS

but it can be applied to other kinds of BSS algorithms,
including time domain BSS. It is helpful in investigating
the acoustical characteristics of BSS in a reverberant
environment.

6.
Fig. 10 Jammer impulse response of BSS system when
non-causal part of the ﬁlter is completely eliminated.

Fig. 11 Jammer impulse response of BSS system when
non-causal part of the ﬁlter is limited to 128 taps.

eliminating it completely. The lower bound of the ﬁlter
length, which can remove direct sound, is much shorter
than the ﬁlter length yielding the best separation performance. Based on PJE in Fig. 6, the proper length of the noncausal part is around 128 taps (corresponding to 16 ms)under our experimental conditions. Figure 11 shows the
jammer impulse response when the non-causal part of theﬁlter is limited to 128 taps. The pre-echo noise and the
direct sound are both removed. Although we just cut oﬀ theseparating ﬁlters with a rectangular window in this experiment, we did not observed any deterioration on the auditory
quality of the separated signals in our preliminary listening
test. From a psychoacoustic viewpoint, the pre-echo of
16 ms is relatively allowable, because a human hearing
system has premasking eﬀect of about 20 ms [23].
5.4. Applicability of Evaluation Method
We have applied our evaluation method to a BSS
algorithm with a diﬀerent non-linear function  anddiﬀerent scaling method in [11], and have conﬁrmed asimilar result to that reported in this paper. We have also
carried out experiments with changing the locations ofsource signals, and have obtained similar results.
BSS with target dereverberation is still an open
problem, and many algorithms will be designed in the
future. Some of them may realize a deconvolution of thetarget signal, and then their characteristics about the target
dereverberation will be diﬀerent from our results. However, our evaluation method can be used for investigating
the characteristics of their performance.
Our method is not limited to frequency domain BSS,

CONCLUSION

We investigated the performance of a separating
system obtained by frequency domain BSS based on ICA
using the impulse responses of target and jammer signals.
As a result, we found the acoustical characteristics of theseparating system. The separating system eliminates the
direct sound of the jammer signal even when the frame
length is relatively short, and it also reduces the reverberation according to the frame length, while the reverberationof the target is not reduced. The performance of the target
dereverberation does not depend on the frame length and isas poor as that of an NBF. Our results provide experimental
conﬁrmation of the equivalence between BSS and ABF.
The jammer reduction performance improves as theframe length increases. However, an overly long frame
length has a detrimental eﬀect on the performance due toaccumulating errors, and the separated signals are damagedby pre-echo noise. To reduce the pre-echo noise, it iseﬀective to shorten the non-causal part of the separatingﬁlters.
Our analysis method is useful for investigating theacoustical characteristics of BSS in a reverberant environment.

ACKNOWLEDGEMENTS
We thank Dr. Hiroshi Saruwatari for valuable discussions. We also thank Dr. Shigeru Katagiri for continuous
encouragement.
REFERENCES[1] A. J. Bell and T. J. Sejnowski, ‘‘An information-maximization
approach to blind separation and blind deconvolution,’’ NeuralComput., 7, 1129–1159 (1995).
[2] S. Haykin, Ed., Unsupervised Adaptive Filtering (John Wiley& Sons, 2000).
[3] A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (John Wiley & Sons, 2001).
[4] T. W. Lee, A. J. Bell and R. Orglmeister, ‘‘Blind source
separation of real world signals,’’ Neural Networks, 4, 2129–
2134 (1997).
[5] J. Xi and J. P. Reilly, ‘‘Blind separation and restoration of
signals mixed in convolutive environment,’’ Proc. ICASSP ’97,
pp. 1327–1330 (1997).
[6] M. Kawamoto, A. Barros, A. Mansour, K. Matsuoka and N.
Ohnishi, ‘‘Real world blind separation of convolved nonstationary signals,’’ Proc. Int. Conf. Independent Component
Analysis and Blind Source Separation (ICA ’99), pp. 347–352(1999).
[7] P. Smaragdis, ‘‘Blind separation of convolved mixtures in thefrequency domain,’’ Neurocomputing, 22, 21–34 (1998).
[8] L. Parra and C. Spence, ‘‘Convolutive blind separation of nonstationary sources,’’ IEEE Trans. Speech Audio Process., 8,125Acoust. Sci. & Tech. 25, 2 (2004)
320–327 (2000).
[9] M. Z. Ikram and D. R. Morgan, ‘‘Exploring permutation
inconsistency in blind separation of speech signals in areverberant environment,’’ Proc. ICASSP ’00, pp. 1041–1044(2000).
[10] S. Araki, S. Makino, T. Nishikawa and H. Saruwatari,‘‘Fundamental limitation of frequency domain blind source
separation for convolutive mixture of speech,’’ Proc. ICASSP’01, pp. 2737–2740 (2001).
[11] R. Mukai, S. Araki and S. Makino, ‘‘Separation and dereverberation performance of frequency domain blind source separation for speech in a reverberant environment,’’ Proc. Eurospeech ’01, pp. 2599–2602 (2001).
[12] F. Asano, S. Ikeda, M. Ogawa, H. Asoh and N. Kitawaki,‘‘Blind source separation in reﬂective sound ﬁelds,’’ Proc. Int.
Workshop Hands-Free Speech Communication (HSC ’01),
pp. 51–54 (2001).
[13] S. Kurita, H. Saruwatari, S. Kajita, K. Takeda and F. Itakura,‘‘Evaluation of blind signal separation method using directivity
pattern under reverberant conditions,’’ Proc. ICASSP ’00,
pp. 3140–3143 (2000).
[14] L. Parra and C. Alvino, ‘‘Geometric source separation:
Merging convolutive source separation with geometric beamforming,’’ Proc. NNSP ’01, pp.273–282 (2001).
[15] K. Torkkola, ‘‘Blind separation of convolved sources based on
information maximization,’’ Proc. NNSP ’96, pp.423–432(1996).
[16] K. Matsuoka and S. Nakashima, ‘‘Minimal distortion principle
for blind source separation,’’ Proc. Int. Workshop Independent
Component Analysis and Blind Signal Separation (ICA ’01),
pp. 722–727 (2001).
[17] S. Araki, S. Makino, R. Mukai and H. Saruwatari, ‘‘Equivalence between frequency domain blind source separation andfrequency domain adaptive null beamformers,’’ Proc. Eurospeech ’01, pp. 2595–2598 (2001).
[18] M. Knaak and D. Filbert, ‘‘Acoustical semi-blind source
separation for machine monitoring,’’ Proc. Int. Workshop on
Independent Component Analysis and Blind Signal Separation(ICA ’01), pp. 361–366 (2001).
[19] S. Amari, A. Cichocki and H.H. Yang, ‘‘A new learningalgorithm for blind signal separation,’’ in Advances in Neural
Information Processing Systems 8 (The MIT Press, 1996),
pp.757–763.
[20] H. Sawada, R. Mukai, S. Araki and S. Makino, ‘‘Polar
coordinate based nonlinear function for frequency-domain
blind source separation,’’ Proc. ICASSP ’02, pp.1001–1004(2002).
[21] F. Asano and S. Ikeda, ‘‘Evaluation and real-time implementation of blind source separation system using time-delayed
decorrelation,’’ Proc. Int. Workshop Independent Component
Analysis and Blind Signal Separation (ICA ’00), pp. 411–415(2000).
[22] D. Schobben, K. Torkkola and P. Smaragdis, ‘‘Evaluation ofblind signal separation methods,’’ Proc. Int. Conf. Independent
Component Analysis and Blind Source Separation (ICA ’99),
pp. 261–266 (1999).
[23] E. Zwicker and H. Fastl, Psychoacoustics Facts and Models(Springer-Verlag, 1990).

126

Ryo Mukai received the B.S. and the M.S.
degrees in information science from the University of Tokyo, Japan, in 1990 and 1992,
respectively. He joined NTT in 1992. From1992 to 2000, he was engaged in research anddevelopment of processor architecture for network service systems and distributed network
systems. Since 2000, he has been with NTT
Communication Science Laboratories, where he is engaged inresearch of blind source separation. His current research interests
include digital signal processing and its applications. He is a memberof the IEEE, ACM, the ASJ, IEICE, and the IPSJ.
Shoko Araki received the B.E. and the M.E.
degrees in mathematical engineering and information physics from the University of Tokyo,
Japan, in 1998 and 2000, respectively. Her
research interests include array signal processing, blind source separation applied to speech
signals, and auditory scene analysis. She is amember of the IEEE and the ASJ.
Hiroshi Sawada received the B.E., M.E. and
Ph.D. degrees in information science from Kyoto
University, Kyoto, Japan, in 1991, 1993 and2001, respectively. In 1993, he joined NTT
Communication Science Laboratories. From1993 to 2000, he was engaged in research on
the computer aided design of digital systems,
logic synthesis, and computer architecture. Since
2000, he has been engaged in research on signal processing and blindsource separation for convolutive mixtures using independent
component analysis. He is a member of the IEEE and the IEICE.
Shoji Makino received the B.E., M.E., andPh.D. degrees from Tohoku University, Japan, in
1979, 1981, and 1993, respectively. He joined
NTT in 1981. He is now an Executive Manager
at the NTT Communication Science Laboratories. His research interests include blind source
separation of convolutive mixtures of speech,
acoustic signal processing, and adaptive ﬁlteringand its applications. He received the Paper Award of the IEICE in
2002, the Paper Award of the ASJ in 2002, the Achievement Awardof the IEICE in 1997, and the Outstanding Technological Development Award of the ASJ in 1995. He is the author or co-author of
more than 170 articles in journals and conference proceedings andhas been responsible for more than 140 patents. He is a member of
the Conference Board of the IEEE SP Society and an Associate
Editor of the IEEE Transactions on Speech and Audio Processing. He
is a member of the Technical Committee on Audio and Electroacoustics as well as Speech of the IEEE SP Society. Dr. Makino is a
Senior Member of the IEEE, a member of the ASJ, and the IEICE.