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MathGroup Archive 1995

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Re: Help about the Fourier transform command

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2086] Re: Help about the Fourier transform command
  • From: rknapp (Robert Knapp)
  • Date: Fri, 29 Sep 1995 01:13:28 -0400
  • Organization: The Santa Fe Institute

In article <DFCFHF.KtF at wri.com> Julien Soulhat <soulhat at grbb.polymtl.ca> writes:

> 		Hello every body,
> 
>   I need help about the Fourier transform (see p.679 of the mathematica 
> manual). I would like to know about the following things:
> 
> 		- the mathematica definition of the Fourier transform,

The definition is given there on page 679:

let a be a list, and n = Length[a];

Fourier[a][[s]] = 
   	b[[s]] = (1/Sqrt[n]) Sum[a[[r]] Exp[2 Pi I (r -1)(s-1)/n],{r,1,n}]

similarily

InverseFourier[b][[r]] = 
	a[[r]] = (1/Sqrt[n]) Sum[b[[s]] Exp[-2 Pi I (r -1)(s-1)/n],{r,1,n}]

The transform is done using the Fast Fourier Transform.

> 		- the method for analysing datas with the Fourier transform

There are so many uses of the discrete Fourier transform in data
analysis that list a few here would be of little use.  I am sure you
can find volumes and volumes on the subject in any scientific library.


Rob Knapp
WRI


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