Re: fft question

[Jean Brefort <jean brefort normalesup org>]

Le dimanche 03 octobre 2010 à 21:22 +0200, Leonard Mada a écrit :
> A last idea:
>
> in order to visualize the spectrum of a "complex" Fourier transform
> (unlike FFT), you need to calculate the module of the result, which
> implies squaring the result.
> [Caution: I think it is called "module" in English.]

Actually, it needs phasing. But this is another story.

> Maybe this is the reason for getting only half the image - maybe
> "complex data" implies the generic Discrete Fourier Transform (DFT),
> and the result is a spectrum containing complex numbers, which needs
> a further transformation in order to be displayed - the modulus
> being displayed instead of the actual DFT.

In the low part of the spectrum I get the correct data, but they are
mirrored, also the first value seems invalid. The high part is also
mirrored. After putting the data in order accordingly to that, I get
something correct. I'm just wondering if this is the expected result.

All series have 8192 points, both the original data and the transformed
data, from the real or complex input. Seems the mirroring does not occur
when complex data are provided. This is anticipated since exp(ix) and
exp(-ix) are not the same, while cos(x) and cos(-x) can't be
distinguished.

Best regards,
Jean


> Sincerely,
>
> Leonard
>
>
> -------- Original-Nachricht --------
> > Datum: Sun, 03 Oct 2010 21:08:00 +0200
> > Von: "Leonard Mada" <discoleo gmx net>
> > An: Jean Brefort <jean brefort normalesup org>, gnumeric-list gnome org
> > Betreff: Re: fft question
>
> > Dear Jean,
> >
> > FFT generates symmetric spectra - basically symmetric mirror images.
> > [The frequencies are mirrored against the central 0.]
> >
> > This seems to be the case in the "real" image.
> >
> > While the "complex" image seems to include only one half,
> > which is the usual way to represent the NMR spectrum.
> > [and more generally any frequency-power spectrum in real life]
> >
> > I do not have though access to go_fft, and I am unsure what
> > "complex data" in your post means.
> >
> > Sincerely,
> >
> > Leonard
> >
> >
> > -------- Original-Nachricht --------
> > > Datum: Sun, 03 Oct 2010 08:41:51 +0200
> > > Von: Jean Brefort <jean brefort normalesup org>
> > > An: Gnumeric List <gnumeric-list gnome org>
> > > Betreff: fft question
> >
> > > Hi,
> > >
> > > I'm a bit puzzled about the output of the go_fft function (actually the
> > > same code as what we have in gnumeric, may be gnumeric might use the
> > > goffice version?). I'm trying to use it to transform an NMR FID to a
> > > spectrum. When I use only the real data, things give the expected
> > > result, but I do not understand the output when I use the complex data
> > > input (see attached images). Is there some FFT expert around?
> > >
> > > Regards,
> > > Jean
> >
> > -- 
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