Re: Re: Fourier transform

• To: mathgroup at smc.vnet.net
• Subject: [mg14021] Re: [mg13954] Re: Fourier transform
• From: "Jens-Peer Kuska" <kuska at linmpi.mpg.de>
• Date: Wed, 16 Sep 1998 14:12:01 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Hi David,

I don't know the code but the restriction of the usual fast Fourier
transfrom to
data sets of length 2^n comes from the radix 2 based integer
representation in the most computers. I think Mathematica is so clever
that it will use the fast version of the fft when ever possible.

You can try it out that
In[1]:=
data=Table[Random[],{i,8,1024},{n,1,i}]; In[3]:=
tm= First /@ (Timing[Fourier[#]] & /@ data); In[5]:=
ListPlot[tm /. Second->1]

gives not  propto N^2 plot with some drastic smaller timing results at
Length[data[k]]==2 ^M_Integer.

Regards
Jens

-----Original Message-----
From: David Annetts <dannetts at laurel.ocs.mq.edu.au> To:
mathgroup at smc.vnet.net
Subject: [mg14021] [mg13954] Re: Fourier transform

>Hi Jens-Peer
>
>> Fourier[] implements a numerical fast fourier transform. That means that
>> the data passed to Fourier[] are  the function values f(t) on the
>> interval t in [0,2Pi) with constant increment. The data are assumed to
>> be periodic in t with period 2Pi.
>
> My understanding was that Fourier implemented a Discrete Fourier
>Transform as a general case, and a Fast Fourier Transform if your data
>length an integer power of 2.
>
>--
> ==================================================================
> David Annetts                                       _____________
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```

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