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3 Abstract This report presents a method to achieve acoustic echo canceling and noise suppression using microphone arrays. The method employs a digital self-calibrating microphone system. The on-site calibration process is a simple indirect calibration which adapts in each specic case to the environment and the electronic equipment used. The method also continuously reduces environmental disturbances such as car engine noise and fan noise. The method is primarily aimed at hands free mobile telephones by suppressing the hands free loudspeaker and car cabin noise simultaneously. The report also contains an evaluation of the impact of echo and noise suppression on a real conversation, accomplished in a car using a microphone array.

4 Contents 1 Introduction 3 2 Working Scheme for the Adaptive Canceling and Noise Suppressing Beamformer Phase 1 - The Gathering Process Calibration signals Phase 2 - The Operating Mode Idle/I-mode Transmit/TX-mode Receive/RX-mode Double Talk/DT-mode Calibration Signal Levels Evaluation Conditions Car Environment Microphone congurations Implementation Algorithm Implementation Normalized Least Mean Square (NLMS) algorithm Fully Connected Neural Network Optimal Least Square solution to the normal equations Evaluation Neural Network -Performance Evaluation Normalized Least Mean Square - Performance Evaluation Calibration process - Calibration Signal Level Noise Suppression, LS-solution - Performance Evaluation Canceling, LS-solution - Performance Evaluation Calibration Sequence Length - Performance Evaluation

5 6 Summary and Conclusions 22 A Figures-Evaluation 24 2

6 Chapter 1 Introduction Near-end speech signal Microphone Near-end speech Acoustic echo Near-end speaker Far-end speech Environment noise Far-end speech signal Loudspeaker Acoustic echo path Figure 1.1: Two-way, handsfree communication, conversation between the far- and near-end speaker. and noise related problems are very common in telephone systems. originates from the far-end speaker and echoes back with a time delay, see gure 1.1, causing perception problems. Perception will be further impaired when the speaker is situated in a noisy car in handsfree mode. Environmental noise can, for instance, originate from engine and fan noise and wind and tire friction. A method to decrease the echo from the far-end speaker during handsfree communication is echo cancellation (EC) [1], and a considerable amount of work has been done in this eld. Most work has been devoted to single microphone solutions [2], although some papers propose systems with two microphones [3, 4]. The 3

7 acoustic echo and noise canceller introduced in [5] is further evaluated here. The method is not based on conventional array theory [6, 7], but relies on an indirect calibration [8] by gathering data from the actual environment. The calibration developed here will take on a slightly dierent form. Dierent adaptive algorithms will be compared and evaluated in this report. The system is aimed at mobile hands free communication systems, and it therefore should also take into account the near eld in a small enclosure. The near eld is dicult to describe in an a-priori model. This brings up the solution of employing gathered signal-information from the real target and jammer positions. Obviously these gathered signals contain useful information about the acoustic environment as well as electronic equipment, such as microphones, ampliers, A/D-converters and anti-aliasing lters. Other important information is the microphone element geometry and other spatial and spectral information inherent in the gathered target and jammer signals. Instead of calculating a large number of statistical a-priori information from the gathered data, we will merely use the signals as they appear during the operating phase. The methods evaluated in this report are a Normalized Least Mean Square (NLMS) algorithm, a fully connected Neural Network algorithm, and an optimal Least Square solution to the normal equations where the gathered data are considered as deterministic signals, i.e. the correlations are estimated directly from the data. 4

8 Chapter 2 Working Scheme for the Adaptive Canceling and Noise Suppressing Beamformer The working scheme for the beamformer can be divided in two phases: phase 1, which is the gathering phase and phase 2, which is the continuous ltering and adaptation phase. During phase 2 the beamformer utilizes the calibration signals gathered in phase Phase 1 - The Gathering Process The gathering phase takes place on-site in the actual environment by emitting representative sequences from each jammer and target position. Array signals for each sequence and channel are memorized in a digital memory bank for subsequent use. All array signals are stored simultaniously in the memory bank. The gathered, multi-channel, memorized signals will be used later to form the input and reference for the beamformer in the operating phase. Since a-priori modeling almost always leads to the loss of some information, the main idea in this straight-forward solution is that the calibration signals themselves \are the best tutor". The calibration signals contain information about the acoustical environment, variations in the electrical equipment, and spatial and frequency responses. During and after the calibration phase some restrictions are, however, imposed: The microphone elements and placement can be chosen arbitrarily, but must not be altered or moved unless a new calibration is made. 5

9 x 1 (t) x 2 (t) Anti-Aliasing and A/D conversion x 1 [n] x 2 [n] x M (t) x M [n] Memory Jammer calibration signals Memory Target calibration signals Figure 2.1: Target calibration signals recording. 6

10 x 1 (t) x 2 (t) Anti-Aliasing and A/D conversion x 1 [n] x 2 [n] x M (t) x M [n] Memory Jammer calibration signals Memory Target calibration signals Figure 2.2: Jammer calibration signals recording. 7

11 The equipment must be time invariant. A fair signal to noise ratio during gathering is necessary. 2.2 Calibration signals The gathered calibration signals must arrive from the desired/unwanted (target/jammer) positions, and the signals must contain approximately the same spectral content as a real target/jammer signal. There are dierent methods to facilitate these conditions. A simple approach is to collect human utterances from the target position. A dierent kind of calibration procedure is to place loudspeakers in the desired/unwanted positions and let the loudspeakers emit, one at a time, at or colored bandlimited noise, or gathered speech (see gures 2.1 and 2.2). 2.3 Phase 2 - The Operating Mode A telephone conversation can be divided into four modes: Idle, Receive, Transmit and Double Talk mode Idle/I-mode During the I-mode only car noise exists, i.e. there is no speech from the near or far-end speaker. Near-end speaker: Far-end speaker: Upper beamformer: Lower beamformer: quiet quiet Copy of LB Adaptation on Environmental noise impinges on each of the microphone elements in the microphone array, and is added with virtual near- and far-end speech signals, i.e. the memorized signals. Note that the noise signals have passed through the same electronic equipment as the memorized signals. The virtually gathered speech signals represent a speaker talking from the correct environment/position and a handsfree loudspeaker, gathered with high SNR. These sets of signals are mixed and comprise the inputs to the adaptive lters (see gure 2.3). The desired signal for the adaptive lters is formed by a suitable combination of the memorized target signals only. The adaptive algorithm now has access to all the information needed to adapt the lters both in the spatial- and frequency-domain. 8

12 The coecients are continuously copied into the upper beamformer/lter which produces the output. Note that the inputs to the upper beamformer contain only signals coming from the microphone elements Transmit/TX-mode During the TX-mode only near-end speech and car noise are present. Near-end speaker: Far-end speaker: Upper beamformer: Lower beamformer: talking quiet Fixed Adaptation o When near-end speech is detected, the adaptation is turned o. Incoming microphone signals from the microphone array are now processed by the xed upper beamformer, using the latest set of lter coecients adapted to the latest actual situation. The lter coecients also suit in all probability the actual disturbance since the situation is short term stationary Receive/RX-mode During the RX-mode, only far-end speech and car noise signals are present. Near-end speaker: Far-end speaker: Upper beamformer: Lower beamformer (LB): quiet talking Copy of LB Adaptation on The algorithm behavior is similar to the I-mode described above. The main dierence is that the microphone signals in this mode consist of real noise and speech from the far-end speaker Double Talk/DT-mode During the DT-mode, near- and far-end speech as well as car noise are present. Near-end speaker: Far-end speaker: Upper beamformer: Lower beamformer: talking talking Fixed Adaptation o In double talk mode, no adaptation is made; the beamformer coecients are xed, and the output from the upper beamformer is transmitted. 9

13 2.4 Calibration Signal Levels During phase 2, the balance (see gure 2.3) between the memorized inputs and microphone inputs to the adapting beamformer can be controlled by: 1. Factor =)Near-end memorized speech signal amplication/attenuation. 2. Factor =)Far-end memorized speech signal amplication/attenuation. 3. Factor =)Incoming environment noise amplication/attenuation for signals from the microphone array. The mix of the components will control the adaptive lter suppression or amplication of sources both in the frequency- and spatial-domain. A large value of and versus will cause the adaptive lter to emphasize cancellation of both the far-end speech and/or car noise. However, too large a suppression will yield degradation of the near-end speech signal. Suitable choices of ; and are values which make the signal levels vary around nominal values with a maximum of 10dB. Extreme choices of ; and can possibly have advantages in some situations. 10

14 Figure 2.3: Balance between inputs during phase 2. 11

15 Chapter 3 Evaluation Conditions 3.1 Car Environment The performance evaluation of the acoustic noise and echo canceling beamformer was made in a Volvo 940 GL station wagon. Data was gathered on a multichannel DAT-recorder with a sample rate of 12 khz, and with a 5 khz bandwidth. In order to facilitate simultaneous driving and recording, a loudspeaker was mounted in the passenger seat to simulate a real person's speaking. 3.2 Microphone congurations The microphones used in the evaluation were high quality Sennheiser microphones, and six of them were mounted at on the visor. The distance between the speaker position and the microphone array was 350 mm. The mounting of the linear array can be seen in gures 3.1 and 3.2. This conguration were used throughout the evaluation. 12

16 Mic:# # # # # # # Figure 3.1: Linear microphone geometry with six microphones. The distance between elements is 50 mm. Figure 3.2: Placement of the Sennheiser microphones, linear mount. 13

17 Chapter 4 Implementation The data gathered from the multichannel DAT recorder was converted into Matlab format, which is a conventionally used mathematics software package. The evaluation part of the report is based on this data and all processing is done in Matlab. 4.1 Algorithm Implementation The lower beamformer according to gure 2.3 has been adapted to a sequence of band-limited noise emitted from the jammer and target positions and actual noise in the car by making a recording of the six microphones. The resulting weights have then been used in the upper beamformer in order to enhance the target speech with regard to echo and noise. In the evaluation of the algorithms the parameter L, used in the following sections, is set to Normalized Least Mean Square (NLMS) algorithm A conventional NLMS algorithm with L lter taps for every microphone is used. The training is done in epochs, i.e. the same training set is used iteratively. The stepsize is normalized to the mean power of all microphone signals, furthermore the stepsize is decreased during epochs. With FIR-lters the output from the upper beamformer is given by MX y [n] = w T mx U m [n] ; (4.1) m=1 14

18 where x U m[n] denotes an L-by-1 input vector from the m-th microphone element in the upper beamformer, and w m denotes the L-by-1 corresponding lter weight vector. Overscript T stands for vector transpose. The total number of lter weights is ML. 4.3 Fully Connected Neural Network A feedforward Neural Network has been used to enhance the speech signal. The Neural Network is a fully connected Multiple Layer Perceptron (MLP) and consists of the input layer, one hidden layer and the output layer. The hidden layer consists of six neurons with bipolar sigmoid transfer functions and the output layer consists of one single neuron with a corresponding linear transfer function. Both the hidden layer and the output layer have corresponding bias weights to each neuron. The network weights are updated by using a conventional supervised backpropagation learning rule in an on-line manner, i.e. the weights are updated at every time sample. As for the NLMS algorithm the training has been done in epochs, and the same normalization and damping of the stepsize during epochs has been used. The output of the upper beamformer when using the MLP is described by y (n) = P p=1 w p f MP m=1 w T m;px U m [n] + b p! + b o where x U m[n] denotes an L-by-1 input vector from the m-th microphone element in the upper beamformer and w m;p denotes the L-by-1 corresponding lter weight vector from input m to neuron p in the hidden layer. Parameter w p represents synaptic weights (scalars) between each of the hidden units and the output. Parameters b p and b o denote adaptive osets or biases, and f() is the sigmoid function. Parameter P is the number of neurons in the hidden layer and M is the number of input signals, i.e. microphones. The number of lter taps for every neuron is P (ML +2)+1which is a factor of six more than with a LMS algorithm. 4.4 Optimal Least Square solution to the normal equations The lters used in the upper beamformer are conventional FIR-lters where the lter weights are found by solving the normal equations. When formulating the normal equations the total correlation matrix R xx is dened as 15

19 R xx = 0 B@ R x1 x 1 R x1 x 2 ::: R x1 x 6 R x2 x 1 R x2 x 2 ::: R x2 x R x6 x 1 R x6 x 2 ::: R x6 x 6 1 CA where R x ixj = 0 B@ r ij (0) r ij (1) r ij (2) ::: r ij (L, 1) r ij (1) r ij (0) r ij (1) ::: r ij (L, 2) r ij (L, 1) r ij (L, 2) ::: ::: r ij (0) 1 CA and r ij (k) = 1 N N,k,1 X n=0 x i (n)x j (n + k) ; k =0;1; ::::L, 1 which is a biased cross-correlation estimator due to the constant normalization factor but gives constant varianse for all lags. This estimator is appropriate for both deterministic and random data, so no decision regarding the form of the data is necessary. Parameter N is the total number of time samples in the correlation estimates. Parameter L is the number of lter taps in the FIR-lters. By arranging the lter vectors w m as a column vector W =[w T 1 w T 2 ::: w T 6] T and formulating a cross-correlation vector between the desired signal d(n) and the input signals x m (n) as G xd =[g 1 g 2 ::: g 6 ] T where g i =[g i (0) g i (1) ::: g i (L,1)] and g i (k) = 1 N N,k,1 X n=0 x i (n)d(n + k) ; k =0;1; ::::L, 1 16

20 the normal equations can be formulated as R xx W = G xd Solving this set of equations gives the optimal least square solution to the beamforming problem, based on the data in the memory bank. 17

21 Chapter 5 Evaluation Performance evaluation from the Volvo is illustrated in Appendix A gures A.1- A.14 Common information for all plots are: Near-end speech, coming from the drivers seat is denoted \ /". Far-end speech echo, i.e. handsfree loudspeaker or jammer speech, is denoted \ /". All signals are within a bandwidth of 5 khz. The calibration signals are at noise within the bandwidth. All sequences are of 8 second duration. All gures begin with 8 second sequence of the unadapted single microphone signal from position 4, i.e. the plain unltered single channel microphone signal. The results are presented as short time (20 ms) power estimates in db. In the adaptation phase (phase 2) the control parameters ; ; can be controlled in order to supress or amplify the sources both in frequency and spatial domains. The Memory-Signal-to-Interference Ratio MSIR is controlled by the ratio between and by: MSIR = 10 log 0 MP B@ MP NP m=0 n=1 ( s Tm[n]) 2 NP m=0 n=1 ( s Jm[n]) CA ;

22 where s T and s J denote the memorized calibration signals for target and jammer, respectively. In the handsfree mode this corresponds to the speaker, usually placed in the front seat, and the handsfree loudspeaker in the middle of the instrument panel, directed towards the driver. The number of microphones in the array, M, is 6, while the number of samples, N, varies between 2400, in the memorized calibration sequence. In addition, the MSNR for the calibration phase is dened as: MSNR = 10 log 0 MP B@ MP NP m=0 n=1 ( s T [n]) 2 NP m=0 n=1 ( s D[n]) 2 where s T and s D denote the memorized calibration signals for the target and the actual ambient disturbances. In the car environment s D corresponds to environmental car noise such as engine-, wind- and tire friction. Keeping xed at 0 db and varying and in db units will aect the MSIR and the MSNR by the same amount. During the ltering phase, or the evaluation mode, the true signal level for the jammer is used, i.e SIR = 0 db, and for noise disturbance, SNR =,5 db has been used in order to make it possible to subjectively decide if any distortion is present. This reduction does not aect the suppression levels in the linear cases at all and these levels are not noticeably aected in the non-linear case. The sound les corresponding to the gures in Appendix A, gures A.1-A.14, are available in.wav- format from Neural Network - Performance Evaluation The Neural Network (MLP) has been trained by using a sequence of 4800 sample records for each input signal and the desired signal. The input signals were created by recording an emission of band-limited at noise from the jammer and target positions and actual noise on the six microphones in the car, while driving. The target (desired) signals were created by doing the same recording on microphone 4 while the car was parked and the emission was done from the target position alone, see gure 2.3. The sequence was iterated for 1000 epochs and the stepsize was damped exponentially from 0.1 in the rst epoch to in the last epoch. The balance parameters,, and were xed at 0 db. The result is shown in gure A.1, and it can be seen that a suppression of approximately 15 db is achieved for both echo and noise. 1 CA ; 19

23 5.2 Normalized Least Mean Square - Performance Evaluation The same conditions have been evaluated for the NLMS algorithm as for the Neural Network. The result is shown in gure A.2. The noise suppression has improved to approximately 17 db when compared to the Neural Network solution, while the echo suppression is the same. A subjective listener test gives no dierences in distortion between the two methods. 5.3 Calibration process - Calibration Signal Level The training sequence used here is the same as with the MLP and the NLMS, while the lter weights have been calculated rather than found by training. The calculation is done by solving the normal equations dened in chapter 4.4. The solution to this set of equations is determined by using Matlab. The balance parameters and are here modied by the same amount while is xed at 0 db. This modication aects the mix of jammer and noise level in contrast to target level in the training sequence. Three settings are compared, (;) = 0dB; 5dB and 10dB. The result can be seen in gures A.3-A.5 which show that these settings have a very little impact on the nal result, when it comes to suppression. Subjective listening shows that the distortion is increased when increasing these levels. In all three cases the damping of both noise and echo is improved by approximately 1-2 db, when compared to the NLMS solution. 5.4 Noise Suppression, LS-solution - Performance Evaluation Pure noise suppression is evaluated by solving the normal equations for a 4800 sample sequence. This calculation is done by emitting band-limited noise from the target position alone, without car noise present, when recording the training sequence. This process is the same as letting =,1 db. The solution is the same as with both echo- and noise suppression except for this modication of the training sequence. Figure A.6 shows the result where echo is present in the sequence and gure A.7 is a ltering without any echo present. The result shows that approximately a 22 db suppression of the noise is achieved while the echo is left almost unsuppressed. 20

24 5.5 Canceling, LS-solution - Performance Evaluation canceling is evaluated in the same manner as with pure noise suppression but with,1db when recording the training sequence. Figures A.8-A.9 show the result with and without noise present (of course, some noise is always present). It can be seen that the noise component is left almost unsuppressed while the echo component is reduced by approximately 25 db. 5.6 Calibration Sequence Length - Performance Evaluation The least square solution to both echo and noise suppression by solving the normal equations is done here with varying length of the training sequence. The balance parameters, and are held at nominal values, i.e. they are at 0 db. Figures A.10-A.14 show the resulting suppression for dierent selections of training sequence length. It can be seen that increasing the training length from samples to gives only slightly better performance. The resulting suppression with a training set of samples is approximately 20 db for both echo and noise. Subjective listening indicates that the distortion is small. 21

25 Chapter 6 Summary and Conclusions The best resulting suppression was approximately 20 db for both echo and noise. This result was achieved by solving the normal equations to the beamforming problem. The structure with non-linearities in the adaptive lter, the Neural Network, gives no extra performance in spite of the large number degrees of freedom, i.e. a factor of six more weights than with the NLMS. The scheme of training the adaptive lter in epochs, for both NLMS and the MLP, and by decreasing the stepsize during epochs, gives better results than by increasing the length of the training set accordingly, compare [5]. Further, by increasing the level of both and in comparison to, when solving the normal equations, no extra echo and noise suppression is attained, while the distortion is increased. The mix between echo canceling and noise suppression can be controlled by the relative levels of disturbance, i.e. by controlling,,. Here, the situations of letting and equal zero are evaluated, respectively. The result is that when equals zero no major echo suppression is attained, and when equals zero no major noise reduction is attained. Approximately 25 db echo suppression is achieved when solving the normal equations for pure echo canceling with correlation estimates based on 4800 data samples. For pure noise suppression with the same conditions approximately 22 db suppression is achieved. Solving the normal equations for a sample training set gives only a slightly better result than for a training set of samples. This indicates that further increasing of the length of the training set may not increase the resulting disturbance suppression. 22

26 Bibliography [1] B.Widrow, S. D. Stearns, \Adaptive Signal Processing", Prentice Hall, [2] M. Sondhi and W. Kellermann, \Adaptive Cancellation for speech signal", Chapter 11 in Advances in Signal Processing, Edited by S. Furui and M. Sondhi, Dekker, New York, [3] Sen M. Kuo, Zhibing Pan, \Adaptive Acoustic Cancellation Microphone", J. Acoust. Soc. Am., vol 93, no 3,March 1993, pp [4] M. Rainer, P. Vary, \Combined acoustic echo cancellation dereverberation and noise reduction: a two microphone approach", Ann. Telecommun., 49, no. 7-8, 1994, pp [5] M. Dahl, I. Claesson, \Acoustic Cancelling with Microphone Arrays", Research Report 2/95, Feb [6] I. Claesson, S. Nordholm, \A Spatial Filtering Approach to Robust Adaptive Beamforming", IEEE Transactions on Antennas and Propagation, vol. 40, no. 9., Sept [7] S. Nordebo, I. Claesson, S. Nordholm, \Adaptive Beamforming: Spatial Filter Designed Blocking Matrix", IEEE Journal of Oceanic Engineering, vol. 19, no. 4, Oct [8] S. Nordebo, I. Claesson, S. Nordholm, B. A. Bengtsson \ `In situ' Calibrated Adaptive Microphone Array", Research Report 2/94, ISSN

27 Appendix A Figures-Evaluation 5 0 Car Noise and Suppression using Fully Connected Neural Network 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.1: Car Noise and Suppression using Fully Connected Neural Network with = 0 db, = 0 db and = 0 db, trained under 1000 epochs with 4800 samples training set 24

28 5 0 Car Noise and Suppression using Normalized LMS 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.2: Car noise and echo Suppression using Normalized LMS algorithm with =0dB, =0dB and =0dB, trained under 1000 epochs with 4800 samples training set 5 0 Car Noise and Suppression using Least Square Optimal filter 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.3: Car Noise and Suppression using Least Square Optimal Filter solved for 4800 samples with =0dB, =0dB and =0dB 25

29 5 0 Car Noise and Suppression using Least Square Optimal filter 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.4: Car Noise and Suppression using Least Square Optimal Filter solved for 4800 samples with =0dB, =5dB and =5dB 5 0 Car Noise and Suppression using Least Square Optimal filter 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.5: Car Noise and Suppression using Least Square Optimal Filter solved for 4800 samples with =0dB, =10dB and =10dB 26

30 5 0 Car Noise Suppression using Least Square Optimal filter 5 10 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.6: Car Noise Suppression using Least Square Optimal Filter solved for 4800 samples with =0dB, =,1 db and =0dB, (echo is present) 5 0 Car Noise Suppression using Least Square Optimal filter 5 10 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.7: Car Noise Suppression using Least Square Optimal Filter solved for 4800 samples with =0dB, =,1 db and =0dB, (no echo present) 27

31 5 Car Suppression using Least Square Optimal filter 0 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.8: Car Suppression using Least Square Optimal Filter solved for 4800 samples with =0dB, =0dB and =,1 db, (noise is present) 5 0 Car Suppression using Least Square Optimal filter 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.9: Car Suppression using Least Square Optimal Filter solved for 4800 samples with = 0 db, = 0 db and =,1 db, (articial noise level at,32 db is added for presentation purposes, actual noise level is controlled by numerical accuracy and becomes approximately,80 db) 28

32 5 0 Car Noise and Suppression using Least Square Optimal filter (Solved for 2400 sampels) 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.10: Car Noise and Suppression using Least Square Optimal Filter solved for 2400 samples with =0dB, =0dB and =0dB 5 0 Car Noise and Suppression using Least Square Optimal filter (Solved for 4800 sampels) 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.11: Car Noise and Suppression using Least Square Optimal Filter solved for 4800 samples with =0dB, =0dB and =0dB 29

33 5 0 Car Noise and Suppression using Least Square Optimal filter (Solved for 7200 sampels) 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.12: Car Noise and Suppression using Least Square Optimal Filter solved for 7200 samples with =0dB, =0dB and =0dB 5 0 Car Noise and Suppression using Least Square Optimal filter (Solved for sampels) 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.13: Car Noise and Suppression using Least Square Optimal Filter solved for samples with =0dB, =0dB and =0dB 30

34 5 0 Car Noise and Suppression using Least Square Optimal filter (Solved for sampels) 5 Output Power [db] One microphone: unadapted Six microphones: adapted Time [s] Figure A.14: Car Noise and Suppression using Least Square Optimal Filter solved for samples with =0dB, =0dB and =0dB 31