Performance comparison of adaptive filtering in time and frequency domain for unmixing acoustic sources in real reverberant environments for close – microphone applications

PERFORMANCE COMPARISON OF ADAPTIVE FILTERING IN TIME AND FREQUENCY DOMAIN FOR UNMIXING ACOUSTIC SOURCES IN REAL REVERBERANT ENVIRONMENTS FOR CLOSE – MICROPHONE APPLICATIONS 2013 MASTER

PERFORMANCE COMPARISON OF ADAPTIVE FILTERING IN TIME AND FREQUENCY DOMAIN FOR UNMIXING ACOUSTIC SOURCES IN REAL REVERBERANT ENVIRONMENTS FOR CLOSE –

MICROPHONE APPLICATIONS

2013

MASTER OF ENGINEERING

Department of Electrical and Electronic Information Engineering

DANG NGUYEN CHAU

M125212

TOYOHASHI UNIVERSITY OF TECHYNOLOGY

PERFORMANCE COMPARISON OF ADAPTIVE FILTERING IN TIME AND

REVERBERANT ENVIRONMENTS FOR CLOSE – MICROPHONE APPLICATIONS

（800 words）

One significant problem in audio recording is microphone leakage That is when the sound of an instrument

or other sources is picked by the microphone other than the desirable sources For example, when a group of

musicians is playing together, the individual microphone will not only take the signal from one instrument but

also capture the interference signals that are generated by other instruments The close-microphone technique,

in which the microphone is placed in close to the source of interest, is used in order to make the microphone

capture as much of the sound of interest as possible and reduce the effect of microphone leakage

The purpose of this work is comparing the performance of two adaptive filtering techniques for solving the

problem of unmixing acoustic sources These two techniques identify channel impulse response based on

minimum mean squared error (MMSE) criterion However, one uses the calculation in frequency domain with

the Wiener filter while the other calculates it in time domain by using NLMS algorithm Besides that, the

calculation in time domain uses the “solo interval”, which is usually used in music performance With the

using of “solo interval”, the two calculations have different performance This work aims examining the

performance the model using NLMS algorithm to the realistic problem of unmixing and separating of two

interfering sources in the several reverberant environments with the close-microphone technique Moreover,

the performance of the model in this work will be compared with the model using Wiener filter, which is

presented as good algorithm for blind source separation (BSS) problem in unmixing acoustic sources

In the experiment, two speakers, which are used to produce the anechoic recording of music from instruments,

are used as the two sources and two omnidirectional microphones are used as the sensors In the music

performance, there are usually time interval that there is only one instrument are in active In this period, the

NLMS algorithm is used to estimate the channel response from this source to another microphone This channel

response could be called as the leakage path response After that period, two of sources are in active The

subtraction of the signal from this microphone with the leakage signal, which is the multiplication of the leakage

path response and the other microphone signal, could be seen as the estimated signal of interest The experiment

is produced in different rooms, which have different time reverberant, for examining the system performance in

various real environments The length of the weighting vector, which is used in this work as the approximation of

the leakage path response, is changed too The result of this changing is used to examine the performance of

system when changing the length of weighting vector

For the performance evaluation, by using the orthogonal projection, the output signal of the system could be

decomposed into three components: a version of the original source signal, the error term that depends on the

interference signal and the other error term that depends on the other noise Two parameters are used to show the

performance of the algorithm is signal-to-interference ratio (SIR) and signal-to-distortion ratio (SDR) The SIR is

used to show the remaining interference signal in the unmixed signal while the SDR is used as the quality

measure of the remaining interference and noise in the output signal

The result of the experimental shows that in the way of SIR, the Wiener filter gives the better performance

than the NLMS algorithm when the distance of source and microphone is low (10cm-25cm) When this distance

increases, the NLMS algorithm give the better performance than the Wiener filter In the other hand, in the way

of SDR, the NLMS algorithm always gives the better performance than the Wiener filter The room reverberation

time also has effect on the algorithm performance The room with longer reverberation time will gives the better

performance in two cases SIR and SDR The weighting vector length has effect on the system performance too

However, the result of this work shows that it is not effective when choosing increasing the weighting vector

length for increasing the performance

1 INTRODUCTION 5

2 ADAPTIVE NOISE CANCELLATION 7

2.1 Wiener filter 8

2.2 Recursive Least Squares (RLS) adaptive filter 12

2.3 The Steepest descent method 15

2.4 The Least Mean Squared (LMS) adaptation method 16

3.PROBLEM FORMULATION 16

4 RELATED WORK 18

5 NLMS ALGORITHM APPROACH FOR UNMIXING ACOUSTIC SOURCES 21

6 PERFORMANCE EVALUATION 24

7 EXPERIMENTAL PROCEDURE 26

8 RESULT 28

8.1 Signal before and after processing 28

8.2 Algorithm performance 30

8.3 Effect of room acoustic 35

8.4 Effect of the length of weighting vector 38

9 CONCLUSION 42

REFERENCE 43

LIST OF FIGURES

Fig.1.1 Microphone leakage in Close-Microphone applications

Fig.2.1 A frequency domain Wiener filter for reducing additive noise

Fig.2.2 Wiener filter structure

Fig.2.3 Illustration of an adaptive filter

Fig.3.1 Block diagram of the blind source separation problem

Fig4.1 Block diagram of Wiener filter

Fig.4.2 Block diagram of Wiener filter for two sources-two microphones case

Fig.5.1 Block diagram of system using NLMS algorithm

Fig.7.1 Reverberant time

Fig.7.2 Learning curve of the NLMS algorithm

Fig.8.1 Clean signal (a), Signal at the microphone (b) and the Output signal of the system (c)

Fig.8.2 System performance (SIR) with recording in room 3 and the 2048 – filter length

Fig.8.3 System performance (SDR) with recording in room 3 and the 2048 – filter length

Fig.8.4 System performance (SIR) with recording in room 1 (a) and room 2 (b) with the 2048 – filter length

Fig.8.5 System performance (SDR) with recording in room 1 (a) and room 2 (b) with the 2048 – filter length

Fig.8.6 System SDR performance and SIR performance of Wiener filter in various room

Fig.8.7 System performance (SIR) of model using NLMS algorithm in various rooms with 2048 – filter

length

Fig.8.8 System performance (SDR) model using NLMS algorithm in various rooms with 2048 – filter length

Fig.8.9 Algorithm performance (SIR) with various weighting vector length in room 1 and room 3

Fig.8.10 Algorithm performance (SDR) with various weighting vector length in room 1 and room

LIST OF TABLES

Table 7.1 Experiment parameter

Table 7.2 Properties of rooms in which recordings took

ACKNOWLEDGEMENT

In the first, I want to say thank you to Prof Uehara, who is my supervisor In the time I am in TUT, Prof Uehara has been helping me everything from problems in the school to the problem in life Prof Uehara has given me the ideas and suggesting, which is really value, for my research Besides that, Prof Uehara has been helped me to have to best condition for finishing my research

Kitayama is my tutor in the time in Japan He is the person who has helped me, who has the first time far from country, to be acquainted with the life in Japan He has always joined the seminar with me, given the ideas for me… I really want to show my thankful to him

Ad-hoc group is one of group in Wireless Communication Laboratory, which is the group I belong

to I want to say thank you to everyone in group for the suggesting in the seminar With your help, I could do

my work more easy

With the other in my Laboratory, I want to say thank you with your friendship All of you are very friendly with the, that make me feel no strange with the new life

Finally, I want to say thank you to Vietnamese friends in TUT You are really good with me

Toyohashi, June 15, 2013

Dang Nguyen Chau

PERFORMANCE COMPARISON OF ADAPTIVE FILTERING IN TIME AND FREQUENCY DOMAIN FOR UNMIXING ACOUSTIC SOURCES IN REAL REVERBERANT ENVIRONMENTS FOR CLOSE –

MICROPHONE APPLICATIONS

1 INTRODUCTION

In the modern music, it often involves a number of musicians playing together inside the same room, with a number of microphones, which are set to capture the sound from their instrument (see Fig.1.1 [1]) A common technique for setting microphones in this situation is to place a dedicated microphone to reproduce each sound source Ideally, the microphone has to pick the only signal from the interested instrument However, due to the effect of the various instruments, the microphones will pick not only the signal from interested source but also the signal from other instruments This is known as the microphone leakage,

which is undesired effect The close-microphone technique is the technique in which the microphone is

placed close to the interested source The microphone is close to the interested source to capture as much of the interested sound as possible and reduce the microphone leakage effect This technique is also used to minimize the effect of the room acoustics on the received signal

Fig.1.1 Microphone leakage in Close-Microphone applications

In order to address this problem, sound engineers suggest some ways: using the directional microphone, optimal placements of sources and microphones… However, the problem is discussed is more general, noting that this problem and the need for source separation and interference suppression arise in various other applications

The purpose of this work is suggesting a model to solve the problem unmixing two interference sources recorded in various reverberant environments with the close-microphone technique Besides that, it

is aimed examining the performance of this model and the model using Wiener filter in [2]

In realistic case, the sources are located in enclose spaces such as concert hall or studio room The source signal arriving at the microphone will be largely dominated by the room impulse response Therefore, under such condition, the system from sources to microphones is the same as a multi input – multi output system This system is the set of room impulse response from the sources to the microphones However, the inversion of this system is not simple The main reasons are given in [2] such as: the non-minimum phase property of room impulse response, the unstable inversion of the system… One more reason is the room impulse response for audio processing is considered as a lengthy filter The inverting for the matrix with each element has ten thousand elements has large computational cost So, it is reasonable for suggesting a model to solve the general problem of unmixing sources Such model is presented in [2] with a model using Wiener filter

Wiener filter is an alternative for solving the problem source separation It provides a way to estimate the interested source s n ˆ( ) from the signalx n ( )which contains the interested signal x n ( ) and interfering signal x n ( ) The Wiener filter is frequently used for the problem source separation NLMS is also frequently used in sound processing However, it is frequently used for noise removing or echo equalization

This work suggests a model using NLMS with the close-microphone set up for unmixing the audio sources The system performance will be compared with the model using Wiener filter Moreover, the system is examined in various real environments for unmixing sources successfully

This work is organized as follows Section 2, the adaptive filters are presented In section 3, the problem formulation is presented After that, the related work is discussed in section 4 In section 5, the suggested model using NLMS algorithm is presented Section 6 is used to discuss about the performance computing In the section 7 and 8, the experimental and results are presented Finally, the conclusion is in section 9

2 ADAPTIVE NOISE CANCELLATION

In telecommunication from noisy acoustic environment, it is often that the interested signal is observed with an additive noise The noisy signal could be modeled as:

wherex m ( )andn m ( ) are the signal and noise, the variablem is the discrete-time index The signalx m ( )could be recovered by subtraction of noise estimate from the noisy signal Fig.2.1 shows an adaptive noise cancellation system with two-input

Fig.2.1 A frequency domain Wiener filter for reducing additive noise

In above system, a microphone takes input noisy signalx m ( )  n m ( ) and the second microphone takes only noise n m (   ).The factor and the time delay provide a simple model of the effect of propagation of noise to different positions in space The noise from second microphone is processed by an adaptive filter to make it equal to the noise contain in the noisy signal of microphone 1 Then, it is subtracted

by the noisy signal to cancellation the noise

Wiener filter is known as the optimal solution for the noise cancellation Besides that, adaptive filters such as: Recursive least square (RLS) adaptive filter, Steepest descent method, Least mean square (LMS) adaptive method are the filters with the coefficients filter get the Wiener solution adaptively

2.1 Wiener filter

Wiener theory, which is formulated by Norbert Wiener, forms the foundation of data-dependent least squared error filters Wiener filter is used in wide range applications such as linear prediction, signal coding, echo cancellation, channel equalization… The coefficients of Wiener filter are calculated by minimizing the average squared distance between the filter output and the desired signal

A Wiener filter (Fig.2.2) is presented by the coefficient vectorw, takes the input signal y m ( )and produces an output signalx m ˆ( ), which is the minimum mean squared estimate of the desired signalx m ( ) The filter input-output relation could be given as:

x m w y m k





Fig.2.2 Wiener filter structure

wheremis the discrete time index The vector yT   y m y m ( ), (  1), , ( y m P   1)  is the input signal of the filter and the vector T  0, 1, , 1

P



w is the Wiener filter coefficients vector

The filter error signal is defined as the different between the desired signal x m ( ) and the filter output x m ˆ( )

whereR yy  Ey( )m y T( )m  is the autocorrelation matrix of the input signal, and ryx  E  y ( ) ( ) m x m  is the cross correlation vector of the input and desired signals

From the equation (2.4), the gradient of the mean squared error function with respect to the filter coefficient vector is given by

To obtain the least mean squared error, we have to set the complex derivate of above function to zero with respect to filter W f ( )

whereP YY( )f  E Y f Y ( ) *( )f is the power spectrum of the input signal and P XY( )f  E X f Y ( ) *( )f 

is the cross power spectrum ofX f ( )andY f ( ) From the equation (2.12), the Wiener filter in frequency domain is described as:

( )( )

( )

XY YY

whereX f ( )andN f ( ) are the spectra of the clean signal the noise The Wiener filter in frequency domain for noise cancellation application could be written as:

( )( )

2.2 Recursive Least Squares (RLS) adaptive filter

Recursive least squared error (RLS) filter is a sample adaptive, time domain, version of Wiener filter, which is presented above The RLS filter has a fast rate of convergence to the optimal coefficients Fig.2.3 shows an illustration of an adaptive filter

Fig.2.3 Illustration of an adaptive filter

Let y m ( ), x m ( ), w ( ) m   w m w m0( ), 1( ), , wP1( ) m  denote the filter input, the desired signal and the filter coefficients vector The filter output could be expressed as:

 

2 2

where R is the autocorrelation matrix of the input signal and yy r is the cross correlation vector of input yx

signal and desired signal

For block N samples vector, the autocorrelation matrix could be written as:

yy T yy

( 1) ( ) ( )

yy T yy

2.3 The Steepest descent method

The mean squared error surface is a quadratic bowl-shaped curve, with a single global minimum that corresponds to the MMSE filter coefficients The steepest descent method is based on taking a number of downward steps in the direction of negative gradient of the error surface Starting with an initial value, the filter coefficients vector is successive updated in the downward direction until the minimum point, which has gradient is zero, is reached The steepest descent method adaptation equation can be expressed as:

where the factor 2 of equation (2.37) is absorbed in the adaptation step size 

Let w0 denote the optimal MMSE filter coefficients vector From the Wiener filter, we have:

where max is the maximum eigenvalue of the autocorrelation matrix of the input signal

2.4 The Least Mean Squared (LMS) adaptation method

The steepest descent method employs the gradient of the squared error to reach the MMSE of the filter coefficients The LMS algorithm is the simpler version of the gradient search In which, the gradient of mean squared error is replaced the gradient of instantaneous squared error function The LMS adaptation method is defined as:

sensors The main problem is finding an approximate inverse system without any prior information about the mixing system or the source signals

Fig.3.1 Block diagram of the blind source separation problem

The problem could be formulated mathematically as follows:

whereN is the number of sources, m  1, , Mwith M is the number of the microphone

The signal s nn( ) is the original source signal from the instrument, x nm( )is the mixture signal at the microphone m and u nm( ) is the additional noise that may be presented The impulse response hmn( ) n

presents the impulse response from the source n to the microphonem With mn, hnn( ) n is the direct impulse response, while mnshows the leakage path impulse response

To simplify the problem, the equation (3.1) could be written as follow:

In this work, the Wiener filter is consider as a special case of BSS algorithm Fig.4.1 [2] shows that

a Wiener filter can be considered for separating audio sources

Fig4.1 Block diagram of Wiener filter

The interested signals n ( )is corrupted by an interfering signalu n ( ) The signal arrives to the microphone could be described as:

ss k uu k

P W

In the close-microphone application, the direct impulse response (from interested source to microphone) could be modeled as an ideal impulse response [2],hnn( ) n   ( ) n Furthermore, the amplitude

of the leakage impulse response is much lower than the direct impulse response

Wiener filter was formulated wide-sense stationary signals The audio signals are non-stationary, thus the Wiener filter in frequency will be used with the STFT implementation [3]

Considering a system with two sources and two microphones (N = M = 2), a model using Wiener filter to estimate the original signal is suggested in [2] (see Fig.4.2)

Fig.4.2 Block diagram of Wiener filter for two sources-two microphones case

The Wiener filter for the signal at the microphone 1 for the two sources – two microphones case could be calculated:

   1 1   

1

s s k k

s s k u u k

P W

Thus, the Wiener filter could be rewritten as:

   1 1    

1

,,

x x k k

P W

The PSDs of the signals at the microphones could be calculated as:

The Wiener filter in equation (4.4) has much lower amplitude than the equation (4.3) However, in this application, this do not effect on the performance of the Wiener filter

Finally, the output signal of the system could be described as:

5 NLMS ALGORITHM APPROACH FOR UNMIXING ACOUSTIC SOURCES

LMS algorithm or NLMS algorithm are very popular due to its low computational cost and easy implementation They are widely used in many application like echo equalization, speech recognition or echo cancellation [4]-[5]

A model is suggested in this work to solve the problem of unmixing signals from two sources In this model, the NLMS algorithm is used to calculate the approximation of the channel impulse response

Fig.5.1 Block diagram of system using NLMS algorithm

In above system, the signals of two sources are and The signals at the microphones are