MATLAB: How to do FT Time shift and Time scaling properties

fft time shifting and scaling

Currently i am trying use matlab to do the FT properties -time shift and time scaling, can someone help me in the implementation? i would like to prove that Timeshift: F[x(t-τ) ]= e^(-jwτ) F[x(t)]
Time scaling: F[x(at)]=1/(|a|) X(w/a)
Thanks.

Best Answer

 t=0:0.001:0.1-0.001;
 Fs = 1e3;
 freq1 = 100;
 x1=cos(2*pi*freq1*t);
 Delay=2;
 yp = fft(x1);
 yp = yp(1:length(x1)/2+1);
 f = 0:Fs/length(x1):500;
 yp = yp.*exp(-1i*2*pi*f*Delay*(1/Fs));
 yp = [yp conj(fliplr(yp(2:end-1)))];
 y = ifft(yp,'symmetric');
 plot(t(1:100),x1(1:100),'b');
 hold on;
 plot(t(1:100),y(1:100),'r');
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