Re: Confused by FFTW output

From: Martin Brown (|||newspam|||_at_nezumi.demon.co.uk)
Date: 03/16/05 

Date: Wed, 16 Mar 2005 10:36:02 +0000

Tom wrote:

> Hi,
> thanks, Martin and James, I see now the flaw related to the symmetry
> and implicit periodicity and now got a spectrum with a negligible
> imaginary part. However, the real part is still different from the
> analytic solution in that it changes sign some times; it is still only
> the absolute value which reproduces the analytic solution (except for
> the scaling factor, of course).
> Here are the first 4 samples:
> Re(F),num |F,num| Re(F),an
> 2.169456 2.169456 1.981664
> -1.369174 1.369174 1.247095
> 0.3386716 0.3386716 0.3108198
> -3.5211481E-02 3.5211481E-02 3.0680126E-02
>
> It's probably trivial, but I don't get what is going on here. Any
> further ideas?

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.

There are several variations on a theme about how the transform is tiled
too. I don't know which one(s) FFTW's real-conjugate sym adopts.

Regards,
Martin Brown

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