MERGE: bug-491577 - Gsl FFT test improvement

[Stefan Westerfeld <stefan space twc de>]

   Hi!

I've spent some time trying to figure out the difference between
Gsl FFT and FFTW. The issue already had a bug report:

http://bugzilla.gnome.org/buglist.cgi?bug_id=491577
 491577 - Gsl FFT code can produce incorrect results

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I think I've found the reason for the difference between Gsl FFT and other
FFTs. While Wikipedia (and FFTW) use

out[k] = SUM{n=0..N-1} (in[n] * exp (-2 * pi * j / N * k * n))

as definition for the FFT, Numerical Recipies (and the Gsl FFT) use (one minus
sign less)

out[k] = SUM{n=0..N-1} (in[n] * exp (2 * pi * j / N * k * n))

so there seems to be no bug here, just a different definition of what we want
to compute. The two versions are relatively easy to convert into each other
(O(n)), and I do it in SpectMorph.

In any case I suggest adding the DFT test, I modified it to match the
"Gsl/Numerical Recipies" formula. Will send a merge request (stwbeast ->
bug-491577).
=======

repo:   http://space.twc.de/public/git/stwbeast.git
branch: bug-491577

   Cu... Stefan
-- 
Stefan Westerfeld, Hamburg/Germany, http://space.twc.de/~stefan