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Ki
Posts:
21
Registered:
5/20/12


about translation in signal with fft
Posted:
Nov 10, 2014 10:56 PM


Hi there, I am trying to test the fft property. The first one I tried is on the translation property
f(x+a) <=> exp(i*a*w)*F(w)
I found one old post here about the same topic http://www.mathworks.com/matlabcentral/newsreader/view_thread/278809
I modify the code a little bit as follows
angfreq = 2*pi*0.01; N = 256; n = 0:N1; %n = (N/2):(N/21); % fail to reproduce the translation property if I use this phi = 1; a = 1; w = 2*pi/N*n;
f = cos(angfreq*n); e = exp(i*w*a); sf = real(ifft(ifftshift(fftshift(fft(f)).*e))); plot(n, f); hold on; plot(n, sf,'r');
The plot shows a perfect translation by 1 unit with the operator exp(i*w*a). There, the fourier frequency is defined as w = 2*pi/N*n; However, in fft should the frequency defines as w = 2*pi/M*[0:N/2, N/2+1:1] such that the zero order goes first, positive frequency follows and then the negative frequencies. However, if I defined it this way by making the n = (N/2):(N/21); I fail to see the correct translation. Why is that?



