CS Project Report

SPEECH ENHANCEMENT BY COMPRESSIVE SENSING Instructor: Dr. Dalei WuProject by:Joseph Antony ChristoperRuoyun LiangWalaaeldin AhmedConcordia UniversityAugust, 20131 AbstractThe proposed Compressive sensing method is a new alternative method used to eliminate noise from the input signal and enhance the quality of the speech signal with fewer samples required for the reconstruction than needed in some of the methods like Nyquist sampling theorem. The basic idea is, the speech signals are sparse in nature and most of the noise signals are non-sparse in nature, and CS eliminates the non-sparse components and reconstructs only the sparse components of the input signal. Experimental results prove that the average segmental SNR (signal to noise ratio) and PESQ (perceptual evaluation of speech quality) scores are better in the compressed domain.2 Introduction:With the increase in the use of mobile phone, laptops etc, communication have taken the next level and the enhancement of signals has become very important. The Nyquist Shannon sampling theorem states that for reconstruction, the input signal must have all frequencies below the Nyquist frequency, which is half the sampling frequency, so one needs to know the information of the signal in advance for reconstruction in this method, obviously large amount of samples are required in Nyquist sampling method and we have to compress them afterwards. CS method combines both compressing and sampling in a single step, and for the reconstruction a small data of non-adaptive linear measurements of the input signal is enough. As the signals can be reconstructed from a fewer measurements than the Nyquist sampling, the storage space and transmission bandwidth are reduced.The CS method is based on the realization that the input signal x (n) has sparse representation.x (n)=Ψ θ(n),Where, Ψ is N × N sparse inducing matrix.As mentioned before, sampling and compression are performed in one step, so the entire CS method can be represented in the following matrix notationy=Фx (n) = ФΨ θ (n),where x(n) is a N × 1 vector and the sensing matrix Ф is a M × N matrix, where M<<N, so the dimension of y(n), which is M × 1 vector is smaller than x(n). Hence sampling and compression are performed in a single step. So by varying the sensing matrix Ф, signals can be perfectly recovered. This can achieved byusing a sensing matrix, which is highly incoherent to the sparsity inducing matrix Ψ, since the measurement process is non-adaptive, the sensing matrix Ф does not depend on the input signal x(n).The last step is the recovery of the original signal, if the original signal x(n) is sparse, and the sensing matrix Ф and sparsity inducing matrix Ψ obey the RIP condition, then original signal x(n) can be reconstructed perfectly.2.1 Compressive Sensing based speech enhancement scheme:Fig. 2.1 shows the basic scheme of CS based speech enhancement. As mentioned previously, the CS method is based on the fact that speech signals are sparse in nature in the time frequency representation whereas noise signals are non-sparse. Speech signals are considered to be sparse in nature, because the speech signals are non-stationary and the speech power is not constant and it varies compared to the average power. Fig shows that the input signal x(n) is first converted to frequency domain representation through STFT block. The STFT converts the input signals in to parallel frequency bands.Figure 2.1: CS based speech enhancement schemeThen these signals are passed through CS block, where the signals are transformed via y=Фx(n) representation, where the sensing matrix Ф can be selected from various choices are CS matrices like partial DCT or Gaussian matrices, in this project we have assumed Ф as a random Gaussian M × N matrix. As mentioned before are M<<N, the dimension of y(n) are reduced compared to x(n), hence compression is performed while the noises are suppressed. And the enhanced output signal is recovered by performing inverse STFT on all frequency bands. In this project for the CS recovery we have used the basis pursuit method. The basis pursuit de-noising formula (BPDN) states thatx’= arg min || y=Фx(n|| + ||λ||Where the de-noising process is controlled only by a single parameter λ. This parameter is called the regularization pa rameter and it controls the sparsity of the output denoised signal x’(n). Small value of λ makes the output less sparse and large value of λ makes the output sparser, so an optimum value of λ should provide a good trade-off between the smoothness of the reconstructed signal and the similarity to the original signal. In our project we have chosen the value for λ as 0.1, and the results demonstrate that both PESQ and SNR are better in the output signal, and both have increased as M/N and the number of STFT points increases.3 Experimental Setup3.1 Experimental SettingsData selected:all_8k_white_db -5.wavall_8k_white_db0.wavall_8k_white_db 5.wavall_8k_white_db10.wavall_8k3.2 ProceduresThe figure 3.2 presents the procedures for the experiments of this project. The music is read by the matlab. The signal thenis converted from analog to digital by the STFT matlab code, and then pass by the CS process using the l1_ls matlab code. After doing the CS, the results will be converted to analog again using the ISTFT matlab code and the SNR and PESQ are then calculated. There are three governing points in this program. First, the lambda value should be decided ,Second, the program should be run using different values of the compression ratio, i.e M/N= 0.1 to 0.9 with increment of 0.1. At last, in order to get the better results, the whole program was run six times for each M/N value to calculate the average of six SNR values and six PESQ values.Deciding Lambda value:On building up the main matlab code and running it several and several times using different values of lambda, it was clear that an acceptable and convenient value of lambda was to be taken as 0.1, this value was then fixed and considered for further measurements after that.3.3 Performance measuresThe PESQ values and SNR values are used to evaluate the performance of the CS based algorithm. The PESQ measure is more accurate in predicting speech distortion of the processed speech whereas the SNR reflects noise suppression more accurately. Both measures give a good indication on noise suppression and speech distortion.Read the music from .wavto matlab Convert the signal from analog to digital(DoingSTFT)Find the GuassianMatrix(A)Find Y (Y=A*X)CS(denoise) Convert the signal from digital to analog(DoingISTFT) Calculate SNR and PESQ Plot 3D figures Decide lambdaFor loop for M/N from 0.1 to 0.9 with increment=0.1Record data 6times Figure 3.2: the flow chat of the project4 Experimental results and discussions4.1 Data ResultsOn running the main matlab code (Appendix-1) 6 times for each compression ratio (M/N = 0.1:0.9),for each sub band (64, 128, 256, 512, 1024), for each signal used (all_8k_white_db -5.wav, all_8k_white_db0.wav, all_8k_white_db 5.wav, all_8k_white_db10.wav), the following results could be obtained using the already mentioned lambda (0.1):all_8k_white_dbminus5all_8k_white_db0.wavall_8k_white_db5.wavall_8k_white_db10.wavThe figures 4.2.1 to 4.2.4 present the PESQ results of -5dB, 0dB, 5dB and 10dB respectively using CSprocess, which is presented withdifferent M/N ratios (0.1:0.9) and different sub bands(64-1024)Figure 4.2.1 for -5dB: PESQ vs. M/N vs. number of sub bands641024Number of SubbandsFigure for -5dB: PESQ vs. M/N vs. number of subbandsM/NP E S QFigure 4.2.2 for 0dB: PESQ vs. M/N vs. number of sub bands64102411.522.533.54Number of SubbandsFigure for 0 dB: PESQ vs. M/N vs. number of subbandsM/NP E S QFigure 4.2.3 for 5dB: PESQ vs. M/N vs. number of sub bands64102411.522.5Number of SubbandsFigure for 5 dB: PESQ vs. M/N vs. number of subbandsM/NP E S QFigure 4.2.4 for 10dB: PESQ vs. M/N vs. number of sub bandsAs it can be seen in the previous figures, The PESQ scores are generally increasing in values as the M/N increases from 0.1 to 0.9102411.52Number of SubbandsFigure for 10 dB: PESQ vs. M/N vs. number of subbandsM/NP E S QThe figures 4.2.5 to 4.2.8 present the SNR results of -5dB, 0dB, 5dB and 10dB respectively using CSprocess, which is presented with different M/N ratios (0.1:0.9) and different sub bands (64-1024)641024-3-2.5-2-1.5-1-0.5Number of SubbandsFigure for -5dB: SNR vs. M/N vs. number of subbandsM/NS e g m e n t a l S N RFigure 4.2.5 for -5dB: SNR vs. M/N vs. number of sub bandsFigure 4.2.6 for 0dB: SNR vs. M/N vs. number of sub bands641024-3.5-3-2.5-2-1.5-1-0.5Number of SubbandsFigure for 0 dB: SNR vs. M/N vs. number of subbandsM/NS e g m e n t a l S N R641024-3-2.5-2-1.5-1-0.5Number of SubbandsFigure for 5 dB: SNR vs. M/N vs. number of subbands M/N S e g m e n t a l S N RFigure 4.2.7 for 5dB: SNR vs. M/N vs. number of sub bandsFigure 4.2.8 for 10dB: SNR vs. M/N vs. number of sub bandsAs it can be seen in the previous figures, The SNR scores are generally increasing in values as the M/N increases from 0.1 to 0.9641024-2.5-2-1.5-1-0.5Number of SubbandsFigure for 10 dB: SNR vs. M/N vs. number of subbandsM/NS e g m e n t a l S N R641024Number of SubbandsFigure for -5dB: SNR vs. PESQ vs. number of subbandsSegmental SNRP E S Q6410241234Number of SubbandsFigure for 0 dB: NSR vs. PESQ vs. number of subbandsSegmental SNRP E S QThe figures 4.2.9 to 4.2.12 present comparisons for PESQ and SNR results for -5dB, 0dB, 5dB and 10dB respectively using CS processand different sub bands (64-1024).Figure 4.2.9 for -5dB: SNR vs. PESQ vs. number of sub bandsFigure 4.2.10 for 0dB: SNR vs. PESQ vs. number of sub bands64102411.522.5Number of SubbandsFigure for 5 dB: SNR vs. PESQ vs. number of subbandsSNRS e g m e n t a l P E S QFigure 4.2.11 for 5dB: SNR vs. PESQ vs. number of sub bandsFigure 4.2.12 for 10dB: SNR vs. PESQ vs. number of sub bands64102411.52Number of SubbandsFigure for 10 dB: SNR vs. PESQ vs. number of subbandsSNRS e g m e n t a l P E S QAs it can be seen in the previous figures, for a higher number of STFT point’s results in a slight increase of both The PESQ and the SNR scores, which is attributed to the increased sparsity of the speech observations as the number of STFT points increases.4.3 Comparison against other conventional speech enhancement methodsThe following figure presents the performance of the proposed CS based speech enhancement is compared against two other conventional methods (OMLSA and MMSELSA methods) using appendix ( 3 ), and as it can be seen in the figure that the CS approach is of smooth nature for different db values.Figure 4.3.1Comparison among other conventional speech enhancement methods-5510dB valueS N RComprision graph among different methods5 ConclusionThe CS’s denoising capabilities are presented by the results of PESQ and SNR. In this project, 1080 SNR values and 1080 PESQ values are recorded. In order to get more accurate results for the final plotting for the SNR and PESQ, each one needed to be measured for 9 M/N values (0.1 to 0.9 ) for 5 sub bands(N=64, 128,256,512 and 1024) six times each,the average number of these six times’ results is calculated for plotting in matlab. The 3D plots for the SNR and PESQ are also made from Excel for good observa tions. The CS’s denoising capabilities are presented by the results of PESQ and SNR. The results of this project proof that the CS has a great incremental contribution on the speech enhancement whereas the method results is compared to two other different methods (OMLSA and MMSELSA methods) to come out with a smoother response for different db values.6 ReferencesSiow Yong Low ,Duc Son Pham , SvethaVenkatesh, 2013. Compressive speech enhancement.Sciverse ScienceDirect Speech Communication 55 (2013) 757–768Dalei Wu, Wei-Ping Zhu, M.N.S Swamy, 2012. IET Signal Processing pp. 1–8, doi: 10.1049/iet-spr.2012.0192 Massimo Fornasier and HolgerRauhut, 2010. Compressive Sensing7 AppendicesAppendix (1):%Codes for Main function:clc;clear all;[d,sr]=wavread('all_8k_white_db5.wav'); % read the data from the music file n = 64; % n will be set to 64, 128,256,512,1024 to get the final datahop = n/4;scf = 1.0;% Calculate the basic STFT, magnitude scaledX = scf * stft(d, n, n, hop); % call the stft function to transfer the% input data from analog to digital[r,m]=size (X); % find the size of input dataa= X(1,:); % the first row of the input data is real number ,% so just copy the original oneb=abs( X(2:r, :)); %the following rows except the first row contain%imaginary number, so chnage the complex number to real%number.X_new = [a;b]; % make the new input wich only contain the real numbersp=floor(0.9*r); % 0.9 is the number for M/N, which will be changed by 0.1% to 0.9 with increament of 0.1 for getting different data.% however, the result should be integer, so the floor is% utlized%find the Gaussian matrixA=rand(p,m);A_new=A/norm(A);Y=(A_new)*X_new'; % Y= Guassian matrix *inputlambda = 0.1; % regularization parameter% we already checked lambda from 0.1 to 1, and find out% 0.1 will get the best results for SNR and PESQ%Doing the CSfor i=1:1:p[cs(:,i),status]=l1_ls(A_new,Y(:,i),lambda); %call the l1_ls function to%do CSend%Calculate the basic ISTFTzero= zeros(m,r-p);CS_new = cat(2,cs,zero);z = istft(CS_new', n, n, hop); % call the istft function to convert the%result back to analog dataFs1=sr;cleanfile='all_8k';[clean,Fs2]=wavread(cleanfile); %get the data from clean file SnR1=calcSegSNR(z',clean,Fs1,Fs2); %calculte SNRdisp(SnR1);SnR2= pesq(clean, z', Fs2); %calculte PESQdisp(SnR2);Appendix (2):%Codes for 3D plots:%Figure for -5dB PESQ vs. M/N vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];Y=[0.1 0.1 0.1 0.1 0.1;0.2 0.2 0.2 0.2 0.2;0.3 0.3 0.3 0.3 0.3;0.4 0.4 0.4 0.4 0.4;0.5 0.5 0.5 0.5 0.5;0.6 0.6 0.6 0.6 0.6;0.7 0.7 0.7 0.7 0.7;0.8 0.8 0.8 0.8 0.8;0.9 0.9 0.9 0.9 0.9];SNR64= [-0.4168,-0.4075, -0.3982, -0.3650, -0.3301, -0.2972,-0.2787,-0.2273, -0.2197];PESQ64= [0.3230, 0.4167, 0.5456, 0.6978, 0.8329, 1.1077, 1.3232, 1.6047,1.6113];SNR128=[-0.5461,-0.5230,-0.4915,-0.4838, -0.4551, -0.4473, -0.4235, -0.3851, -0.3801];PESQ128=[0.9545, 1.2044, 1.2645, 1.4580, 1.6640, 1.7507, 2.1328, 2.5974,2.6892];SNR256=[-0.8993, -0.8633, -0.8484, -0.8297, -0.7845, -0.7035, -0.7731, -0.5865, -0.5466];PESQ256=[1.1345, 1.2575, 1.5497, 1.7595, 1.8268, 1.9907, 2.3091, 2.5678,2.6990];SNR512= [-2.6620, -2.3384, -2.1704, -1.8792, -1.7752, -1.5975, -1.2763, -1.0596, -0.9786];PESQ512= [1.0226, 1.1457, 1.3541, 1.5705, 1.7174, 1.9723, 2.2966, 2.6541,2.7766];SNR1024=[-3.4948, -3.3940, -3.1965, -3.0919, -2.8784, -2.6324,-2.2239,2.0790, -1.6329];PESQ1024= [1.2862, 1.4834, 1.6577, 1.7346, 1.9900, 2.2107, 2.3760, 2.5545,2.9741];Z= [PESQ64;PESQ128;PESQ256;PESQ512;PESQ1024];mesh(X,Y',Z);axis([64 1024 0.1 0.9 min(min(Z)) max(max(Z)) ]);set(gca,'XTick',[64 128 256 512 1024]);set(gca,'xscale','log') ;xlabel('Number of Subbands');ylabel('M/N');zlabel('Segmental SNR');title('Figure for -5dB: PESQ vs. M/N vs. number of subbands',...'FontWeight','bold')%Figure for -5dB: SNR vs. M/N vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];Y=[0.1 0.1 0.1 0.1 0.1;0.2 0.2 0.2 0.2 0.2;0.3 0.3 0.3 0.3 0.3;0.4 0.4 0.4 0.4 0.4;0.5 0.5 0.5 0.5 0.5;0.6 0.6 0.6 0.6 0.6;0.7 0.7 0.7 0.7 0.7;0.8 0.8 0.8 0.8 0.8;0.9 0.9 0.9 0.9 0.9];SNR64= [-0.4168,-0.4075, -0.3982, -0.3650, -0.3301, -0.2972,-0.2787,-0.2273, -0.2197];PESQ64= [0.3230, 0.4167, 0.5456, 0.6978, 0.8329, 1.1077, 1.3232, 1.6047,1.6113];SNR128=[-0.5461,-0.5230,-0.4915,-0.4838, -0.4551, -0.4473, -0.4235, -0.3851, -0.3801];PESQ128=[0.9545, 1.2044, 1.2645, 1.4580, 1.6640, 1.7507, 2.1328, 2.5974,2.6892];SNR256=[-0.8993, -0.8633, -0.8484, -0.8297, -0.7845, -0.7035, -0.7731, -0.5865, -0.5466];PESQ256=[1.1345, 1.2575, 1.5497, 1.7595, 1.8268, 1.9907, 2.3091, 2.5678,2.6990];SNR512= [-2.6620, -2.3384, -2.1704, -1.8792, -1.7752, -1.5975, -1.2763, -1.0596, -0.9786];PESQ512= [1.0226, 1.1457, 1.3541, 1.5705, 1.7174, 1.9723, 2.2966, 2.6541,2.7766];SNR1024=[-3.4948, -3.3940, -3.1965, -3.0919, -2.8784, -2.6324,-2.2239,-2.0790, -1.6329];PESQ1024= [1.2862, 1.4834, 1.6577, 1.7346, 1.9900, 2.2107, 2.3760, 2.5545,2.9741];Z= [SNR64;SNR128;SNR256;SNR512;SNR1024];mesh(X,Y',flipud(Z));axis([64 1024 0.1 0.9 min(min(Z)) max(max(Z)) ]);set(gca,'XTick',[64 128 256 512 1024]);set(gca,'xscale','log') ;xlabel('Number of Subbands');ylabel('M/N');zlabel('Segmental SNR');title('Figure for -5dB: SNR vs. M/N vs. number of subbands',...'FontWeight','bold')%Figure for -5dB: SNR vs. PESQ vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];SNR64= [-0.4168,-0.4075, -0.3982, -0.3650, -0.3301, -0.2972,-0.2787,-0.2273,-0.2197];%a=flipdim(SNR64,2);SNR128=[-0.5461,-0.5230,-0.4915,-0.4838, -0.4551, -0.4473, -0.4235, -0.3851,-0.3801];%b=flipdim(SNR128,2);SNR256=[-0.8993, -0.8633, -0.8484, -0.8297, -0.7845, -0.7035, -0.7731, -0.5865, -0.5466];%c=flipdim(SNR256,2);SNR512= [-2.6620, -2.3384, -2.1704, -1.8792, -1.7752, -1.5975, -1.2763, -1.0596, -0.9786];%d =flipdim(SNR512,2);SNR1024=[-3.4948, -3.3940, -3.1965, -3.0919, -2.8784, -2.6324,-2.2239,-2.0790, -1.6329];%e=flipdim(SNR1024,2);Y=[SNR64 ;SNR128 ;SNR256 ;SNR512 ;SNR1024];PESQ64= [0.3230, 0.4167, 0.5456, 0.6978, 0.8329, 1.1077, 1.3232, 1.6047,1.6113];%a1=flipdim(PESQ64,2);PESQ128=[0.9545, 1.2044, 1.2645, 1.4580, 1.6640, 1.7507, 2.1328, 2.5974, 2.6892];%b1=flipdim(PESQ128,2);PESQ256=[1.1345, 1.2575, 1.5497, 1.7595, 1.8268, 1.9907, 2.3091, 2.5678, 2.6990];%c1=flipdim(PESQ256,2);PESQ512= [1.0226, 1.1457, 1.3541, 1.5705, 1.7174, 1.9723, 2.2966, 2.6541, 2.7766];%d1 =flipdim(PESQ512,2);PESQ1024= [1.2862, 1.4834, 1.6577, 1.7346, 1.9900, 2.2107, 2.3760, 2.5545, 2.9741];%e1=flipdim(PESQ1024,2);Z=[PESQ64 ;PESQ128 ;PESQ256 ;PESQ512 ;PESQ1024];mesh(X,Y,(Z));axis([64 1024 min(min(Y)) max(max(Y)) min(min(Z)) max(max(Z)) ]);set(gca,'XTick',[64 128 256 512 1024]);set(gca,'xscale','log') ;xlabel('Number of Subbands');ylabel('Segmental SNR');zlabel('PESQ');title('Figure for -5dB: SNR vs. PESQ vs. number of subbands',...'FontWeight','bold')%Figure for 0 dB: SNR vs. M/N vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];Y=[0.1 0.1 0.1 0.1 0.1;0.2 0.2 0.2 0.2 0.2;0.3 0.3 0.3 0.3 0.3;0.4 0.4 0.4 0.4 0.4;0.5 0.5 0.5 0.5 0.5;0.6 0.6 0.6 0.6 0.6;0.7 0.7 0.7 0.7 0.7;0.8 0.8 0.8 0.8 0.8;0.9 0.9 0.9 0.9 0.9];SNR64 = [-0.0871,-0.1194,-0.1259,-0.1292,-0.1311,-0.1393,-0.148,-0.1501,-0.152];a=flipdim(SNR64,2);SNR128 = [-0.2851,-0.3048,-0.312,-0.3407,-0.3521,-0.3678,-0.3793,-0.3886,-0.4141];b=flipdim(SNR128,2);SNR256 = [-0.4936,-0.5679,-0.5811,-0.6295,-0.7286,-0.8033,-0.9027,-0.9908,-1.1956];c=flipdim(SNR256,2);SNR512 = [-1.7002,-1.8116,-1.8409,-1.881,-1.953,-2.0415,-2.1675,-2.2124,-2.4466];d =flipdim(SNR512,2);SNR1024 = [-2.805,-2.914,-3.1593,-3.2972,-3.3363,-3.4663,-3.5373,-3.6574,-3.7886];e=flipdim(SNR1024,2);Z=[a;b;c;d;e];mesh(X,Y',flipud(Z));axis([64 1024 0.1 0.9 min(min(Z)) max(max(Z)) ]);set(gca,'XTick',[64 128 256 512 1024]);set(gca,'xscale','log') ;xlabel('Number of Subbands');ylabel('M/N');zlabel('Segmental SNR');title('Figure for 0 dB: SNR vs. M/N vs. number of subbands',...'FontWeight','bold')%Figure for 0 dB: PESQ vs. M/N vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];Y=[0.1 0.1 0.1 0.1 0.1;0.2 0.2 0.2 0.2 0.2;0.3 0.3 0.3 0.3 0.3;0.4 0.4 0.4 0.4 0.4;0.5 0.5 0.5 0.5 0.5;0.6 0.6 0.6 0.6 0.6;0.7 0.7 0.7 0.7 0.7;0.8 0.8 0.8 0.8 0.8;0.9 0.9 0.9 0.9 0.9];PESQ64 = [2.01,1.9363,1.8643,1.716,1.5685,1.43,1.2024,1.0142,0.6903];a=flipdim(PESQ64,2);PESQ128 = [3.2383,2.6862,2.3722,2.0078,1.7707,1.5496,1.4769,1.3632,1.1192]; b=flipdim(PESQ128,2);PESQ256 = [2.6264,2.2056,2.0506,1.971,1.5032,1.1304,0.9284,0.8161,0.7839]; c=flipdim(PESQ256,2);PESQ512 = [4.286,3.5616,2.5783,2.0358,1.4507,1.0744,1.0396,0.9529,0.8173];d =flipdim(PESQ512,2);PESQ1024= [4.5257,4.4285,3.9082,2.8412,2.5779,2.2825,1.7514,1.6415,1.4952];e=flipdim(PESQ512,2);Z=[a;b;c;d;e];mesh(X,Y',(Z));axis([64 1024 0.1 0.9 min(min(Z)) max(max(Z)) ]);set(gca,'XTick',[64 128 256 512 1024]);set(gca,'xscale','log') ;xlabel('Number of Subbands');ylabel('M/N');zlabel('Segmental SNR');title('Figure for 0 dB: PESQ vs. M/N vs. number of subbands',...'FontWeight','bold')%Figure for 0 dB: NSR vs. PESQ vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];SNR64 = [-0.0871,-0.1194,-0.1259,-0.1292,-0.1311,-0.1393,-0.148,-0.1501,-0.152];a=flipdim(SNR64,2);SNR128 = [-0.2851,-0.3048,-0.312,-0.3407,-0.3521,-0.3678,-0.3793,-0.3886,-0.4141];b=flipdim(SNR128,2);SNR256 = [-0.4936,-0.5679,-0.5811,-0.6295,-0.7286,-0.8033,-0.9027,-0.9908,-1.1956];c=flipdim(SNR256,2);SNR512 = [-1.7002,-1.8116,-1.8409,-1.881,-1.953,-2.0415,-2.1675,-2.2124,-2.4466];d =flipdim(SNR512,2);SNR1024 = [-2.805,-2.914,-3.1593,-3.2972,-3.3363,-3.4663,-3.5373,-3.6574,-3.7886];e=flipdim(SNR1024,2);Y=[a ;b ;c ;d ;e];PESQ64 = [2.01,1.9363,1.8643,1.716,1.5685,1.43,1.2024,1.0142,0.6903];a1=flipdim(PESQ64,2);PESQ128 = [3.2383,2.6862,2.3722,2.0078,1.7707,1.5496,1.4769,1.3632,1.1192]; b1=flipdim(PESQ128,2);PESQ256 = [2.6264,2.2056,2.0506,1.971,1.5032,1.1304,0.9284,0.8161,0.7839]; c1=flipdim(PESQ256,2);PESQ512 = [4.286,3.5616,2.5783,2.0358,1.4507,1.0744,1.0396,0.9529,0.8173]; d1 =flipdim(PESQ512,2);PESQ1024= [4.5257,4.4285,3.9082,2.8412,2.5779,2.2825,1.7514,1.6415,1.4952]; e1=flipdim(PESQ1024,2);Z=[a1 ;b1 ;c1 ;d1 ;e1];mesh(X,Y,(Z));axis([64 1024 min(min(Y)) max(max(Y)) min(min(Z)) max(max(Z)) ]);set(gca,'XTick',[64 128 256 512 1024]);set(gca,'xscale','log') ;xlabel('Number of Subbands');ylabel('Segmental SNR');zlabel('PESQ');title('Figure for 0 dB: NSR vs. PESQ vs. number of subbands',...'FontWeight','bold')%Figure for 5 dB: SNR vs. M/N vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];Y=[0.1 0.1 0.1 0.1 0.1;0.2 0.2 0.2 0.2 0.2;0.3 0.3 0.3 0.3 0.3;0.4 0.4 0.4 0.4 0.4;0.5 0.5 0.5 0.5 0.5;0.6 0.6 0.6 0.6 0.6;0.7 0.7 0.7 0.7 0.7;0.8 0.8 0.8 0.8 0.8;0.9 0.9 0.9 0.9 0.9];SNR64=[-0.1204 -0.1003 -0.0697 -0.0492 -0.0478 -0.0455 -0.0310 -0.0212 -0.0141];% SNR64=[-2.1204 -2.1003 -1.9697 -1.0492 -0.9478 -0.6455 -0.4310 -0.212 -0.0141];%a=flipdim(PESQ64,2);SNR128=[-0.3452,-0.2971,-0.2711,-0.2597,-0.2304,-0.1898,-0.1758,-0.1767, -0.1727];%b=flipdim(PESQ128,2);SNR256=[-0.4431,-0.3771,-0.3032,-0.2649,-0.2542,-0.2068, -0.1372,-0.1149,-0.0997];%c=flipdim(PESQ256,2);SNR512=[-1.3059,-1.2145,-0.9984,-0.9043,-0.8095,-0.7215,-0.7112,-0.7013, -0.6899];%d =flipdim(PESQ512,2);SNR1024=[-3.0008,-2.8735,-2.2243,-2.0566,-1.9438,-1.8949,-1.8675,-1.8115,-1.8012];%e=flipdim(PESQ1024,2);Z=[SNR64;SNR128;SNR256;SNR512;SNR1024];mesh(X,Y',(Z));axis([64 1024 0.1 0.9 min(min(Z)) max(max(Z)) ]);set(gca,'XTick',[64 128 256 512 1024]);set(gca,'xscale','log') ;xlabel('Number of Subbands');ylabel('M/N');zlabel('Segmental SNR');title('Figure for 5 dB: SNR vs. M/N vs. number of subbands',...'FontWeight','bold')%Figure for 5 dB: PESQ vs. M/N vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];Y=[0.1 0.1 0.1 0.1 0.1;0.2 0.2 0.2 0.2 0.2;0.3 0.3 0.3 0.3 0.3;0.4 0.4 0.4 0.4 0.4;0.5 0.5 0.5 0.5 0.5;0.6 0.6 0.6 0.6 0.6;0.7 0.7 0.7 0.7 0.7;0.8 0.8 0.8 0.8 0.8;0.9 0.9 0.9 0.9 0.9];PESQ64=[0.5211,1.2265,1.5392,1.9324,1.9404,1.9816,2.1948,2.2062,2.3411];%a=flipdim(PESQ64,2);PESQ128=[0.8521,0.8677,1.2336,1.7328,2.2682,2.3974,2.6810,2.7921,2.8730];%b=flipdim(PESQ128,2);PESQ256=[0.7727,0.9879,1.0710,1.5435,2.0826,2.1193,2.1431,2.2908,2.4005];%c=flipdim(PESQ256,2);PESQ512=[0.6933,0.7965,0.9776, 1.0398,1.4092,1.7162,1.9619,2.1132,2.1293];%d =flipdim(PESQ512,2);PESQ1024=[0.9512,1.2569,1.3221,1.5746,2.1165, 2.2342, 2.3437,2.4587,2.4790]; %e=flipdim(PESQ1024,2);Z=[PESQ64;PESQ128;PESQ256;PESQ512;PESQ1024];mesh(X,Y',Z);axis([64 1024 0.1 0.9 min(min(Z)) max(max(Z)) ]);set(gca,'XTick',[64 128 256 512 1024]);set(gca,'xscale','log') ;xlabel('Number of Subbands');ylabel('M/N');zlabel('Segmental SNR');title('Figure for 5 dB: PESQ vs. M/N vs. number of subbands',...'FontWeight','bold')%Figure for 5 dB: SNR vs. PESQ vs. number of subbands:clc;clear all;X=[64 64 64 64 64 64 64 64 64;128 128 128 128 128 128 128 128 128;256 256 256 256 256 256 256 256 256;512 512 512 512 512 512 512 512 512;1024 1024 1024 1024 1024 1024 1024 1024 1024];SNR64=[-0.1204 -0.1003 -0.0697 -0.0492 -0.0478 -0.0455 -0.0310 -0.0212 -0.0141];%a=flipdim(PESQ64,2);SNR128=[-0.3452,-0.2971,-0.2711,-0.2597,-0.2304,-0.1898,-0.1758,-0.1767, -0.1727];。