Re: [Maxima-discuss] Fourier Transform , almost symbolic

[Gunter K. <gu...@pe...>]

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A second try with a real keyboard:

AFAIK if you calculate the fourier transforma of a fourier transform
of a function you will get a scaled copy of the function so the
inverse fourier transform might not be a this complicated task.

Kind regards,

       Gunter.

On 02.12.2014 17:47, Gunter Königsmann wrote:
> I assume adding a inverse fft will be less work than it seems: for 
> discrete data (and I understood that your transform is dealing
> with discrete data) the inverse fft is the same fourier transform
> but with a different scaling factor.
> 
> Kind regards,
> 
> Gunter.
> 
> 
> 
> On 2. Dezember 2014 16:21:34 MEZ, "Stavros Macrakis (???????
> ????????)" <mac...@al...> wrote:
> 
> Sounds like interesting work, but why is your email in oversized
> boldface with forced carriage returns every few words? That makes
> it unpleasant to read.
> 
> -s
> 
> 
> On Tue, Dec 2, 2014 at 7:22 AM, Edward Montague
> <qui...@gm... <mailto:qui...@gm...>> wrote:
> 
> This relates to sampled data , being quite common nowadays.
> 
> If we look at the Analytical Fourier Transform of a rectangular
> pulse we obtain the now very familiar Sinc function . Using the
> shift theorem for a train of rectangular pulses , all of the same
> width , we obtain a series of complex exponential terms ; all
> multiplied by the Sinc function for the single centered rectangular
> pulse.
> 
> Symbolically simplifying the complex exponential series we arrive
> at a complex Fourier function that completely describes the train
> of , variable amplitude rectangular pulses . This exhibits all of
> the properties of the continuous Fourier Transform for such a
> series .
> 
> This I have implemented , in wxMaxima ; the Inverse Fourier
> Transform might be derived in a similar way , whilst recognizing 
> that the pulse width is the reciprocal of that in the other
> domain. I have yet to complete the Inverse Fourier Transform , I
> ran out of motivation. The inverse fft of the Symbolic Fourier
> Transform appears to return a correct numerical representation of
> the original pulses.
> 
> Is this a valid approach , from first principles it appears to be
> valid , of course the digital computation might have a few
> surprises.
> 
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