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

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

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 (Σταῦρος Μακράκης)" <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...>
>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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