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## Defining a domain over a period 2Pi and More

Asked by Balachandra

### Balachandra (view profile)

on 14 Nov 2013
Latest activity Edited by Balachandra

### Balachandra (view profile)

on 14 Nov 2013

When defining a sine wave in matlab, do we choose a domain [1:N]/N or [0:N-1]/N; These two domains differ by a grid point. However, stuff gets complicated when we take FFT. If I define

N = 128;
x = [0:N-1]/N;
f = sin(2*pi*x);
F = fftshift(fft(f));
F(end+1) = 0;
F = flipdim(F,2);
F = F(1:end-1);
f_inv = -real(ifft(ifftshift(F)));
norm(f-f_inv,'fro');
plot(f,'b*');
hold on
plot(f_inv,'r*');

2) However, if I defined

x = [1:N]/N;

and do the rest same, I get a sine wave in the final which is offset by 2 bins. Why so? and Which is correct?

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