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Re: Re: FFT

• To: mathgroup at smc.vnet.net
• Subject: [mg12849] Re: [mg12834] Re: FFT
• From: David Withoff <withoff>
• Date: Wed, 17 Jun 1998 00:27:52 -0400
• Sender: owner-wri-mathgroup at wolfram.com

> norman at galois.uoregon.edu wrote:
> >
> > Does anyone know where i can find a package implementing the Fast
> > Fourier Transform (discrete version) in Mathematica?
> >
> > Thanks,
> >
> > Bill
>
> It is in the Calculus`FourierTransform` package.
>
> Be aware that this is a standard fft such as the EE folks use and does
> not obey the same set of theorems that Fourier Transforms (Central
> Ordinate theorem,Scaling, etc.) are supposed to obey, so typically
> there is a little bit of work you have to do on the transformed results
> before they are quantitatively useful for anything.

I interpreted your question to mean that you were looking for a separate
package that implements the fast Fourier transform algorithm, perhaps
for pedantic purposes.  I don't know of such a package myself, but I
hope that someone else can point you to one.

As others have already pointed out, if you just want to get the result
of the discrete Fourier transform you can use the built-in Fourier
function, which, like nearly all discrete Fourier transform functions
these days, uses the fast Fourier transform algorithm.  

Regarding the recently contributed comments, however, I did want to
point out that the functions in the Calculus`FourierTransform` package
do  not implement the fast Fourier transform algorithm or any other
algorithm  for computing a discrete Fourier transform.  The functions
in this  package implement the Fourier integral transform, which is a
different   operation.  There is nothing analogous to the fast Fourier
transform algorithm for computing Fourier integral transforms.  The
only version of the fast Fourier transform algorithm is the discrete
version.

Regarding the comments about theorems and quantitative work and such,
all of these transforms are fairly standard, and so will satisfy all
relevant theorems, and other than the care that one should always
exercise in quantitative work, no special effort is needed when using
these transforms.

Dave Withoff
Wolfram Research

• Follow-Ups:
  • Re: Re: Re: FFT
    • From: Sean Ross <seanross@worldnet.att.net>