EC 6120 and EC 5102 DSP MATLAB PROGRAMS DAY 4

AUTO AND CROSS- CORRELATION OF SIGNAL, NOISE AND NOISY SIGNAL

clear all; clc; close all

%Auto correlation and cross correlation fumctions

N = 96;

n = 1 : N;

x = cos(0.25 *pi *n);

rx = conv(x,fliplr(x));

disp('ACF of X=')

min(min(corrcoef(x,x)))

k = -28 : 28;

subplot(3,1,1);

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));

disp('ACF of Y=')

min(min(corrcoef(y,y)))

subplot(3,1,2);

stem (k,ry(68 : 124));

xlabel(' log index');

ylabel(' Amplitude');

title (' clean signal ACF');

rw=conv(w,fliplr(w));

disp('ACF of W=')

min(min(corrcoef(w,w)))

subplot(3,1,3);

stem(k,rw(68 : 124));

xlabel(' log index');

ylabel(' Amplitude');

title(' clean signal ACF');

rxw=conv(x,fliplr(w));

disp('CCF of X with W=')

min(min(corrcoef(x,w)))

figure

subplot (3,1,1);

stem (k,rxw(68 : 124));

xlabel(' log index');

ylabel(' Amplitude');

title (' X with W');

rxy=conv(x,fliplr(y));

disp('CCF of X with Y=')

min(min(corrcoef(x,y)))

subplot (3,1,2);

stem (k,rxy(68 : 124));

xlabel(' log index');

ylabel(' Amplitude');

title (' X with Y');

ryw=conv(y,fliplr(w));

disp('ACF of Y with W=')

min(min(corrcoef(y,w)))

subplot (3,1,3);

stem (k,rxy(68 : 124));

xlabel(' log index');

ylabel(' Amplitude');

title (' Y with W');

LTI SYSTEM PLOT USING ZERO-POLE-GAIN TRANSFER FUNCTION

clear all; clc; close all

% for IIR butterworth LPF of order 3 and .5 cut off

[z,p,k] = butter(3,.5);

h=zpk(z,p,k); tf(h)

[num,den] = tfdata(h,'v')

% [b,a] = butter(3,.5)

[h,w]=freqz(num,den,2^8);% considering 8 bits

plot(w/(2*pi),20*log10(h))

title('LTI response plot')

figure

subplot(2,1,1), plot(abs(h))

title('magnitude')

axis tight

subplot(2,1,2), plot(w*360/(2*pi))

title('Phase converted to degree')

axis tight

DISCRETE FOURIER TRANSFORM

clear all; clc; close all

%Simple DFT without using the FFT algo of MATLAB

N = 256;

n = 1: N;

xn = cos(0.2 *pi *n);

figure(1);

plot(n,xn);

wn = exp(-j* pi/N);

g= 1;

for k = 1: N,

n= 1:N;

xk(g,1) =xn * (wn * ones(N,1)).^(n' * k);

g = g +1;

end

X1 = abs(xk);

figure(2);

plot(n/(2*N),X1/max(X1));

grid;

axis([0,0.5,0,1]);

title('DFT');

xlabel('Frequency in pi unit');

ylabel('Mag');

COMPARISON OF THE dft USING THE EQUATION AND USING MATLAB’S IN BUILT FFT BASED DFT

clear all; clc; close all

%comparing DFT with the in built FFT of MATLAB

N = 256;

n = 1 : N;

xn = cos(0.2 *pi *n);

figure(1);

plot(n,xn);

M=N;

m=0:(M-1);

y = fft(xn,M);

magy=abs(y);

wn = exp(-j* pi/N);

g= 1;

for k = 1: N,

n= 1:N;

xk(g,1) =xn*(wn*ones(N,1)).^(n'*k);

g = g +1;

end

X1 = abs(xk);

figure(2);

subplot(2,1,1);

plot(n/(2*N),X1/max(X1));

grid;

axis([0,0.5,0,1]);

title('DFT');

xlabel('Frequency in pi unit');

ylabel('Mag');

subplot(2,1,2);

plot(m/M,magy/max(magy));

grid;

axis([0,0.5,0,1]);

title('DFT with fft function');

xlabel('Frequency in pi unit');

ylabel('Mag');

COMPARISON OF MULTIPLICATION IN FREQUENCY DOMAIN WITH CONVOLUTION IN TIME DOMAIN

clear all; clc; close all

%showing multiplication in frequency is convolution in time

x=[1 2 3 4];%1st sequence

h=[1 2 1 2];%2nd sequence

l=length(x)+length(h)-1;%length of convolution o/p

xe=fft(x,l);%fft of 1st squence using zero padding

he=fft(h,l);%fft of 2nd squence using zero padding

y1=ifft(xe.*he);%ifft of the prodct of two sequences

y2=conv(x,h);% normal covoluton o/p

error=y1-y2;%error between the two convolutions

k=0:l-1;

subplot(3,1,1),stem(k,y1);

subplot(3,1,2),stem(k,y2);

subplot(3,1,3),stem(k,abs(error));