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+//Example 5.4

+clear;

+clc ;

+close ;

+x = [1,2,3,4,5,2,3,1];

+disp(x,"x[n]=");

+//DFT Computation

+X = fft (x , -1);

+//Display sequence X[k] in command window

+disp(X,"X[k]=");

+

+//Finding time shifted input sequence x[n-2]

+y=x;

+for i=1:2

+    a=y(1);

+    for j=1:length(y)-1

+        y(j)=y(j+1);

+     end

+     y(length(y))=a;

+end

+disp(y,"x2[n]=x[n-2]=");

+//using Time-shifting property

+X2=[zeros(1:8)];

+w=-%i;

+for j=1:8

+    X2(j)=[(w)^(j-1)]*X(j);

+end

+disp(X2,"Using time-shifting property,DFT of x[n-2]=X2[k]=");