DSP MATLAB programs MATLAB Programs as per Exercises

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Saturday, February 20, 2010

Correlation and Convolution

**************************************%covolution of two sequences & %comparison with conv command**************************************x=[1 4 2 4 1 1];h=[1 2 3 4 5];len1=length(x);len2=length(h);len=len1+len2-1;a=fliplr(h);for i=1:lenc(i)=0;for j=1:len1if j>icontinue;endif(len2-i+j)<=0continue;endc(i)=c(i)+(x(j)*a(len2-i+j));end

endk=1:len;conv_op1=c(1:len)subplot(2,1,1),stem(k,conv_op1);title('Without using "conv" command')conv_op2=conv(x,h)subplot(2,1,2),stem(k,conv_op2)

**************************************% correlation using Convolution**************************************N = 96;n = 1 : N;x = cos(0.25 *pi *n);rx = conv(x,fliplr(x));k = -28 : 28;subplot(5,1,1);stem(k,rx(68 : 124));xlabel(' log index');ylabel(' Amplitude');title(' clean signal ACF');w=rand(1,N)-0.5;y=x+w;ry=conv(y,fliplr(y));subplot(5,1,2);stem (k,ry(68 : 124));xlabel(' log index');ylabel(' Amplitude');title (' noisy signal ACF');rw=conv(w,fliplr(w));subplot(5,1,3);stem(k,rw(68 : 124));xlabel(' log index');ylabel(' Amplitude');title(' noise ACF');rxw=conv(x,fliplr(w));subplot (5,1,4);stem (k,rxw(68 : 124));xlabel(' log index');ylabel(' Amplitude');title (' clean signal and noise CCF');rxy=conv(x,fliplr(y));subplot (5,1,5);stem (k,rxy(68 : 124));xlabel(' log index');ylabel(' Amplitude');title (' clean and noisy signal CCF');

**************************************% correlation and Correlation coefficient**************************************N = 96;n = 1 : N;x = cos(0.25 *pi *n);rx = xcorr(x);corrcoef(x)k = -28 : 28;subplot(5,1,1);stem(k,rx(68 : 124));xlabel(' log index');ylabel(' Amplitude');title(' clean signal ACF');w=rand(1,N)-0.5;y=x+w;ry=xcorr(y);corrcoef(y)subplot(5,1,2);stem (k,ry(68 : 124));xlabel(' log index');ylabel(' Amplitude');title (' noisy signal ACF');rw=xcorr(w);corrcoef(w)subplot(5,1,3);stem(k,rw(68 : 124));xlabel(' log index');ylabel(' Amplitude');title(' noise ACF');rxw=xcorr(x,w);corrcoef(x,w)subplot (5,1,4);stem (k,rxw(68 : 124));xlabel(' log index');ylabel(' Amplitude');title (' clean signal and noise CCF');rxy=xcorr(x,y);corrcoef(x,y)subplot (5,1,5);stem (k,rxy(68 : 124));xlabel(' log index');

Posted by SMD at 5:08 AM 36 comments Links to this post

Discrete Time Stable LTI Systems

**************************************%Linearity Property of two sequences**************************************n=0:40; a=2; b=-3;x1=cos(2*pi*0.1*n);x2=cos(2*pi*0.4*n);x=a*x1+b*x2;ic=[0 0];num=[2.2403 2.4908 2.2403];den=[1 -0.4 0.75];y1=filter(num,den,x1,ic);y2=filter(num,den,x2,ic);y=filter(num,den,x,ic);yt=a*y1+b*y2;d=y-yt;subplot(3,1,1), stem(n,y); gridsubplot(3,1,2), stem(n,yt); gridsubplot(3,1,3), stem(n,d); grid

**************************************%shift Invariance property**************************************n=0:40;D=10;x=3*cos(2*pi*0.1*n)-2*cos(2*pi*0.4*n);xd=[zeros(1,D) x];num=[2.2403 2.4908 2.2403];den=[1 -0.4 0.75];ic=[0 0];y=filter(num,den,x,ic)yd=filter(num,den,xd,ic)d=y-yd(1+D:41+D);subplot(3,1,1),stem(y),grid;subplot(3,1,2),stem(yd),grid;subplot(3,1,3),stem(d),grid;

**************************************%To check stability of a system**************************************num=[1 0.8];den=[1 1.5 .9];N=200;h=impz(num,den,N+1);sum=0;n=0:N;for k=1:N+1if abs(h(k))<10^(-6);

breakendsum=sum+h(k);endstem(n,h); grid;disp('Value='),disp(sum) Posted by SMD at 5:01 AM 0 comments Links to this post

Signal Generation

**************************************% generate unit step sequence for N=20. %Plot discrete values and level it.**************************************N=20;xn=ones(1,N);n=0:1:N-1;subplot(2,1,1),stem(n,xn);subplot(2,1,2),plot(n,xn);xlabel('n');ylabel('xn');title('Unit Step Sequence');**************************************% Plot an exponential sequence (0.7)^n % **************************************N=20;n=0:1:N-1;xn=0.7.^n;subplot(2,1,1),stem(n,xn);subplot(2,1,2),plot(n,xn);xlabel('n');ylabel('xn');title('Exponential Sequence');**************************************% Plot an sinusoidal sequence **************************************N=50;n=0:1:N-1;xn=cos(0.2*pi.*n);subplot(2,2,1),stem(n,xn);subplot(2,2,2),plot(n,xn);xlabel('n');ylabel('xn');title('Sinusoidal Sequence');xn=sin(0.2*pi.*n);subplot(2,2,3),stem(n,xn);

subplot(2,2,4),plot(n,xn);xlabel('n');ylabel('xn');title('Sinusoidal Sequence');**************************************% Addition of two sinusoidal sequence % x= sin(0.2*pi*n) + sin (0.5*pi*n) **************************************N=50;n=0:1:N-1;xn= sin(0.3*pi.*n) + sin(0.7*pi.*n); subplot(2,1,1),stem(n,xn);subplot(2,1,2),plot(n,xn);xlabel('n');ylabel('xn');title('Addition of two Sinusoidal Sequence');**************************************% triangular wave generation**************************************y=0:0.5:2;for j=0:3x=(4*j)+y;plot(x,y)hold onendfor k=0:3;x=(4*k)-yplot(x,y)hold onendhold off**************************************%sawtooth wave generation**************************************y=0:.5:2for j=0:8a=(2*j)+yplot(a,y,'b')hold onendx=2:2:18for k=0:.01:2;b=k;plot(x,b,'b')hold onendhold off

**************************************% generation of square wave**************************************y=0:.001:2;for j=0:2:12;x=y;plot(j,x,'r');hold on;endfor k=0:4:12;x=k+y;m=2;plot(x,m,'r')hold onendfor k=2:4:12;x=k+y;m=0;plot(x,m,'r');hold on;endhold offaxis([0 12 -0.5 2.5])**************************************% Aliasing**************************************N=100;n=0:1:N-1;xn=3*cos(0.2*pi.*n);subplot(3,1,1);plot(n,xn);grid;xlabel('n');ylabel('xn');x1n=3*cos(2.2*pi.*n);subplot(3,1,2);plot(n,x1n);grid;xlabel('n');ylabel('x1n');x2n=3*cos(4.2*pi.*n);subplot(3,1,3);plot(n,x2n);grid;xlabel('n');ylabel('x2n');title('Sinusoidal Sequence');

Posted by SMD at 4:57 AM 0 comments Links to this post

Saturday, July 18, 2009

Adaptive filters

function LMSADF%Program to illustrate adaptive filtering using the LMS algorithms

% X delayed input data vector % Y measured signal % W coefficient vector % E enhanced signal

N=30; % filter length M=0; % delay w0=1; % initial value for adaptive filter coefficients SF=2048; % factor for reducing the data samples - 11 bit ADC assumed mu=0.04;X = zeros(N,1); delay = zeros(1,M+1);W = w0*ones(N,1);in = fopen('ADF.dat','r'); %read input data from specified data fileY = fscanf(in,'%g',inf)/SF;fclose(in);if w0==0sf = SF; % scaling factor for displayelsesf = SF/N/w0;end for i=1:length(Y) if M>0 delay(2:M+1) = delay(1:M); % shift data for delayenddelay(1) = Y(i); X(2:N) = X(1:N-1); % update buffer X(1) = delay(M+1);E(i) = Y(i)-W'*X; % the enhanced signalW = W + 2*mu*E(i)*X; % update the weightsendsubplot(2,1,1),plot(1:length(Y),Y*SF); title('Input Signal');subplot(2,1,2),plot(1:length(E),E*sf); title('Enhanced Signal');

====================================================

function UDUADF

% program to illustrate adaptive filtering using % the RLS algorithm via the UDU factorization

% X delayed input data vector % Y measured signal % W coefficient vector % E enhanced signal

clear all;

N = 30; % filter length M = 1; % delay npt = N*(N+1)/2;SF = 2048; % 12-bit ADC scaling p0 = 0.05;w0 = 1;gamma = 0.98;RemoveMean = 0; % 1 - remove the mean from the data, 0 - otherwise

delay = zeros(1,M);U=zeros(1,npt);U(1)=p0;W = w0*ones(N,1);X = zeros(N,1);for i=1:N-1 ik=(i*(i+1)-2)/2+1; U(ik)=p0;end

if w0==0sf = SF; % scaling factor for displayelsesf = SF/N/w0;end

in = fopen('ADF.dat','r'); %read input data from specified data fileY = fscanf(in,'%g',inf)/SF;fclose(in);

if RemoveMean % remove the mean from the data if requiredY = Y - sum(Y)/length(Y);end

for i=1:length(Y) if M>0 delay(2:M+1) = delay(1:M); % shift input data in delay registers

enddelay(1) = Y(i); X(2:N) = X(1:N-1); % update bufferX(1) = delay(M+1);E(i) = Y(i) - X'*W; % the enhanced signalW = uduflt(W,X,U,E(i),gamma ,N);endsubplot(2,1,1),plot(1:length(Y),Y*SF); title('Input Signal');subplot(2,1,2),plot(1:length(E),E*sf); title('Enhanced Signal');

==========================================function w=uduflt(w,x,u,ek,gamma,N)% udu algorithm - a numerically stable form of % the recursive least squares algorithm % % inputs: % x() input vector % dn latest input data value % w() coefficient vector % u() vector containing elements of U and D % % outputs: % en error signal % yn digital filter output % w() updated coefficient vector % u() updated elements of U and D %

sf = 1/gamma;

m=1; % update the UD elements v=zeros(1,N);v(1)=x(1);for j=2:N v(j)=x(j); for k=1:j-1 m=m+1; v(j)=v(j)+u(m)*x(k); end m=m+1; b(j)=u(m)*v(j);endb(1)=u(1)*x(1);alpha=gamma+b(1)*v(1);delta=1/alpha;u(1)=u(1)*delta;

m=1;for j=2:N beta1=alpha; alpha=alpha+b(j)*v(j); p=-v(j)*delta; delta=1/alpha; for k=1:j-1 m=m+1; beta=u(m); u(m)=beta+b(k)*p; b(k)=b(k)+b(j)*beta; end m=m+1; u(m)=u(m)*beta1*delta*sf;endperr=ek/alpha;for j=1:N % update the weights w(j)=w(j)+b(j)*perr;end

============================================function SQRTADF % program to illustrate adaptive filtering using % the square root RLS algorithm

% X delayed input data vector % Y measured signal % W coefficient vector % E enhanced signal

N = 30; % filter length M = 1; % delay npt = N*(N+1)/2;SF = 2048; % 12-bit ADC scaling p0 = 0.05;w0 = 1;gamma = 0.98;RemoveMean = 0; % 1 - remove the mean from the data, 0 - otherwise

delay = zeros(1,M);W = w0*ones(N,1);X = zeros(N,1);S = zeros(1,npt);S(1)=p0;for i=1:N-1 ik=(i*(i+1)-2)/2+1;

S(ik)=p0;end

if w0==0sf = SF; % scaling factor for displayelsesf = SF/N/w0;end

in = fopen('ADF.dat','r'); %read input data from specified data fileY = fscanf(in,'%g',inf)/SF;fclose(in);

if RemoveMean % remove the mean from the data if requiredY = Y - sum(Y)/length(Y);end

for i=1:length(Y) if M>0 delay(2:M+1) = delay(1:M); % shift input data in delay registersenddelay(1) = Y(i); X(2:N) = X(1:N-1); % update bufferX(1) = delay(M+1);E(i) = Y(i) - X'*W; % the enhanced signal

W = sqrtflt(W,X,E(i),S,gamma,N);endsubplot(2,1,1),plot(1:length(Y),Y*SF); title('Input Signal');subplot(2,1,2),plot(1:length(E),E*sf); title('Enhanced Signal');

==================================================

function w=sqrtflt(w,x,perr,s,gamma,N)

% A simple square root RLS adaptive filter % For details, see: % Digital Signal Processing: A Practical Approach % E C Ifeachor and B W Jervis, Pearson, 2002

forgt=sqrt(gamma);sig=forgt;sigsq=forgt*forgt;ij=1; ji=1;for j=2:N fj=0.0;

for i=1:j-1 ji=ji+1; fj=fj+s(ji)*x(i); end a=sig/forgt; b=fj/sigsq; sigsq=sigsq+fj*fj; sig=sqrt(sigsq); a=a/sig; g(j)=s(ji)*fj; s(ji)=a*s(ji); for i=1:j-1 ij=ij+1; sqp=s(ij); s(ij)=a*(sqp-b*g(i)); g(i)=g(i)+sqp*fj; end ij=ij+1;endw = w + g'*perr/sigsq;

=============================function RLSadf % program to illustrate adaptive filtering using % the RLS algorithm

% X delayed input signal% Y measured signal% W coefficient vector % E enhanced signal

N = 30; % filter length M = 1; % stages of delay SF = 2048; % 12-bit ADC scaling p0 = 0.05;w0 = 100;gamma = 0.98;RemoveMean = 0; % 1 to remove the mean, 0 otherwiseW = w0*ones(N,1); % adaptive filter weightsX = zeros(N,1); delay = zeros(1,M+1);P = p0*diag(ones(1,N),0);if w0==0sf = SF; % scaling factor for displayelsesf = SF/N/w0;

end

in = fopen('ADF.dat','r'); %read input data from specified data fileY = fscanf(in,'%g',inf)/SF;fclose(in);

if RemoveMean % remove the mean from the data if requiredY = Y - sum(Y)/length(Y);end

for i=1:length(Y) if M>0 delay(2:M+1) = delay(1:M); % shift input data in delay registersenddelay(1) = Y(i); X(2:N) = X(1:N-1); % update bufferX(1) = delay(M+1); E(i) = Y(i) - X'*W; % the enhanced signalG = P*X/(gamma + X'*P*X); P = (P - G*X'*P)/gamma; W = W + G*E(i); % update the weightsendsubplot(2,1,1),plot(1:length(Y),Y*SF); title('Input Signal');subplot(2,1,2),plot(1:length(E),E*sf); title('Enhanced Signal');Posted by Swanirbhar at 7:10 AM 2 comments Links to this post

Multirate digital signal processing

% % m-file to illustrate simple interpolation and % decimation operations (Program 9B.1, p641)% File name: prog9b1.m % An Illustration of interpolation by a factor of 4 %Fs=1000; % sampling frequencyA=1.5; % relative amplitudesB=1;f1=50; % signal frequenciesf2=100;t=0:1/Fs:1; % time vectorx=A*cos(2*pi*f1*t)+B*cos(2*pi*f2*t); % generate signaly=interp(x,4); % interpolate signal by 4stem(x(1:25)) % plot original signalxlabel('Discrete time, nT ')ylabel('Input signal level')figurestem(y(1:100)) % plot interpolated signal.xlabel('Discrete time, 4 x nT')ylabel('Output signal level')==========================================

% % m-file to illustrate simple interpolation and

% decimation operations (Program 9B.2, p644).% File name: prog9b2.m% An Illustration of sampling rate changes using upfirdn by a factor of 4%Fs=1000; % sampling frequencyA=1.5; % relative amplitudesB=1;f1=50; % signal frequenciesf2=100;t=0:1/Fs:1; % time vectorx=A*cos(2*pi*f1*t)+B*cos(2*pi*f2*t); % generate signaly=resample(x,4,1); % interpolate signal by 4stem(x(1:25)) % plot original signalxlabel('Discrete time, nT ')ylabel('Input signal level')figurestem(y(1:100)) % plot interpolated signal.xlabel('Discrete time, 4 x nT')ylabel('Interpolated output signal level')y1=resample(y,1,4);figurestem(y1(1:25)) % plot decimated signal.xlabel('Discrete time, nT')ylabel('Decimated output signal level')

============================================function moptimum %Program moptimum is for designing I-stage optimum decimator %or interpolator (I=1,2,3 or 4). The program computes the decimation %factors, filter characteristics, and decimator efficiencies

%The following parameters must be provided by the user: % Fs - input sampling frequency % M - overall decimation factor % fp - passband edge frequency % dp - overall passband deviation in +ve dB % ds - overall stopband deviation in +ve dB

clear all;Fs = 96000; % sampling frequency in Hzfp = 450; % passband edge frequency in Hzdp = 0.0864; % overall passband deviation in +ve dBds = 60; % overall stopband deviation in +ve dBM = 96; % overall decimation factor

EvalNStageDecimator(Fs,fp,dp,ds,M); % evaluate single stage decimatorfor i=2:4 % evaluate all possible 2-, 3- and 4-stage decimatorsR = GetFactors(M,i);for j=1:size(R,1);EvalNStageDecimator(Fs,fp,dp,ds,R(j,:));endend

===============================================% % m-file for working out the computational

% complexities of a 2-stage decimator % Program name: mrate-ex1.m % dp=0.01;ds=0.01; dp1=dp/2;ds1=ds;fp=5000;Fi=1536000; F0=12000;M=Fi/F0; M1=16; M2=8;F1=Fi/M1; F2=F1/M2;fs1=F1-(Fi/(2*M)); fs2=F2-(Fi/(2*M));df1=(fs1-fp)/Fi; df2=(fs2-fp)/F1;NUM= -10*log10(dp1*ds1)-13;N1=(NUM/(14.6*df1)); N2=(NUM/(14.6*df2));MPS=(N1*F1 + N2*F2); TSR = N1+N2;M1M2fs1fs2df1df2N1N2MPS======================================function DecimationFactors = GetFactors(M,n) % The function GetFactors finds all possible decimation factors for% 2-, 3-, and 4-stage decimation. M is the% overall decimation factor and n is the number of stages

p = floor(M/(2^(n-1)));m = 1;for i=2:pfor j=2:pif n==2&i*j==MR(m,1) = i; % get the 2-stage decimator factorsR(m,2) = j;m = m + 1;elseif n>2for k=2:pif n==3&i*j*k==MR(m,1) = i; % get the 3-stageR(m,2) = j; % decimator factorsR(m,3) = k;m = m + 1;elseif n>3for l=2:pif i*j*k*l==MR(m,1) = i; % get the 4-stage R(m,2) = j; % decimator factorsR(m,3) = k;R(m,4) = l;m = m + 1;endendend

endendendendR = fliplr(sort(R')'); % sort the decimation factor vectorsz = zeros(1,size(R,2));k = 1;for i=1:size(R,1) % reject the redundanciesfor j=i+1:size(R,1)if R(i,:)==R(j,:)R(j,:) = z;endendif R(i,:)~=zDecimationFactors(k,:) = R(i,:);k = k + 1;endend

==========================================================function decimation%program performs multi-stages of decimation on data in a user-specified data file %enough data must be guaranteed when using a large overall decimation fator

clear all;

r = [2 2 3 2]; % decimation factor array for different stagesFIR = 0; % 1 - use FIR filter, 0 - use IIR filtern = 0; % order of IIR filter or FIR filter length% n=0 for 30 points FIR filter or 8th order Chebyshev type I LPF filterin = fopen('decimation.dat','r') ;[x,count] = fscanf(in,'%g',inf); % data to be decimatedy = x;fclose(in);for i=1:length(r)if n==0 %decimating data use default filterif FIRy = decimate(y,r(i),'fir'); elsey = decimate(y,r(i));endelseif FIRy = decimate(y,r(i),n,'fir'); elsey = decimate(y,r(i),n);endendendplot(1:count,x,1:prod(r):count,y(1:length(y)),'o');

===========================================================function EvalNStageDecimator(Fs,fp,dp,ds,R) format long;a1 = 0.005309;

a2 = 0.07114; a3 = -0.4761; a4 = -0.00266;a5 = -0.5941; a6 = -0.4278; a7 = 11.01217; a8 = 0.51244;dp = 10^(dp/20.0)-1; ds = 10^(-ds/20.0); Ftemp = Fs;

dp = dp/length(R);MPS = 0; TSR = 0;fprintf('stage\tfactor\tFi\tfp\tfs\tdp\tds\tN\n');for i=1:length(R) % n=size(R,1) possible k-stages decimatorsF = Ftemp/R(i);fs = F - Fs/2/prod(R);df = (fs - fp)/Ftemp;Ftemp = F;N = round((log10(ds)*(a1*log10(dp)^2+a2*log10(dp)+a3)+...a4*log10(dp)^2+a5*log10(dp)+a6)/df-df*(a7+a8*(log10(dp)-log10(ds)))+1);fprintf('%d\t%d\t%d\t%d\t%d\t%-7.4f\t%-7.4f\t%d\n',i,R(i),F,fp,fs,dp,ds,N);MPS = MPS + N*F;TSR = TSR + N;endfprintf('MPS = %d, TSR = %d\n\n',MPS,TSR);format;

========================function interpolation %program performs multi-stages interpolation on data in a user-specified data file

clear all;

r = [2 1 1]; % decimation factor array for different stagesl = 4; % filter length alpha = 0.5; % cut-off frequency in = fopen('decimation.dat','r') ;[x,count] = fscanf(in,'%g',inf); % data to be decimatedy = x;fclose(in);for i=1:length(r)y = interp(y,r(i),l,alpha);endsubplot(1,2,1);stem(x);subplot(1,2,2);stem(y);

Posted by SMD at 7:06 AM 0 comments Links to this post Older Posts Home

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