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>