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 _____________ > http://www.ocs.mq.edu.au/~dannetts/ |C R C A M E T| > |-------------| > |_____ | > CRC for Australian Mineral |````` \ | > Exploration Technologies |`````/$\ | > Earth Sciences |````/$$$\____| > Macquarie University, NSW 2109 |```/$$$/.....| > AUSTRALIA |``/$$$/......| > phone: +(1-61-2) 9850 9280, fax (1-61-2) 9850 8366 ------------- > ================================================================== > > >