MATLAB CODE TO VERIFY TIME SHIFTING PROPERTY OF DFT

CODE:

close all;

x=input('Enter the input sequence');

n=input('Enter the delay integer');

x1=length(x);

xn=x1+n;

for i=1:xn;

    if(i<=n)

        xn0(i)=0;

    else

        xn0(i)=x(i-n);

    end;

end;

subplot(2,1,1);

stem(x);

title('Input sequence');

xlabel('time index');

ylabel('amplitude');

subplot(2,1,2);

stem(xn0);

title('delayed sequence');

xlabel('time index');

ylabel('amplitude');

figure;

w=0:pi/xn:pi*(xn-1)/xn;

X=fft(x,length(w));

Xn0=fft(xn0,length(w));

s=exp(-j*w*n).*X;

subplot(2,1,1);

stem(abs(Xn0));

title('DFT of the delayed sequence');

xlabel('time index');

ylabel('amplitude');

subplot(2,1,2);

stem(abs(s));

title('DFT of the original sequence*(e^-j*w*n)');

xlabel('time index');

ylabel('amplitude');

OUTPUT:

Enter the input sequence[1 1 2 2 3 3 4 4 0 0]

Enter the delay integer3