Re: Confused by FFTW output

From: Steven G. Johnson (stevenj_at_alum.mit.edu)
Date: 03/17/05 

Date: Wed, 16 Mar 2005 19:23:12 -0500

Martin Brown wrote:
> Yes. Your final answer is f'(j) = f(j).(-1)^j
>
> The true phase zero or centre for the transform is n/2 cells.
> Correct the coeficients by abs() in FFT space and then invert the
> transform and you will see what I mean.

The sign oscillations are indeed caused by the fact that he centered his
Gaussian at n/2 rather than at 0 (a shift in time domain corresponds to
a linear phase in frequency domain).

However, his magnitudes are still going to be off because of a failure
in his basic assumption: the DFT of a Gaussian is not a Gaussian. His
"analytic" solution is wrong.

Steven

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