# Time shifting property DTFT

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Ch My on 4 May 2017
Answered: Sk Group on 27 Oct 2021
I am suppose to verify the time shifting property of DTFT, by letting x(n) = random sequence uniformly distributed between [0,1] over 0 <= n <= 20 and y(n) = x(n-2). Following is my code, however the plot did not shift by delay of 2. Can anyone help to rectify? Thank you.
clc, clear all, close all;
x=rand(1,21);n=0:20;
k=0:20;w=(pi/20)*k;
X=x*(exp(-1i*pi/500)).^(n'*k);
y=x;m=n+2;
Y=y*(exp(-1i*pi/500)).^(m'*k);
Y1=(exp(-1i*2).^w).*X;
subplot(2,2,1);plot(n,abs(fftshift(X)));
subplot(2,2,2);plot(n,abs(fftshift(Y)));

Santhana Raj on 4 May 2017
I suppose this is what you want to do:
clc, clear all, close all;
x=rand(1,21);n=0:20;
k=0:20;w=(pi/20)*k;
X=x*(exp(-1i*pi/500*n'*k));
y=x;m=n+2;
Y=y*(exp(-1i*pi/500*n'*k));
subplot(1,2,1);plot(n,abs(X));
subplot(1,2,2);plot(m,abs(Y));
Ch My on 4 May 2017
Thank you, but after trying i still did not see y(n) being delayed by 2.

Sk Group on 27 Oct 2021

Sk Group on 27 Oct 2021
Time shifting Prove: DFT{x(n-l)} = X(K)e^(-j(2*pi/N)kl