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From: james@crc.ricoh.com (James Allen)
Subject: Re: Arbitrary N FFT code
Message-ID: <1995Jan27.081559.1724@crc.ricoh.com>
Summary: Radix-2 may be suboptimal for small N
Organization: RICOH California Research Center
References: <3fopac$n63@news.iastate.edu> <790963413snz@jkms.demon.co.uk> <slworkD30u4n.GMM@netcom.com>
Date: Fri, 27 Jan 95 08:15:59 GMT
Lines: 21
Xref: glinda.oz.cs.cmu.edu comp.dsp:16226 sci.image.processing:12196

In <slworkD30u4n.GMM@netcom.com> slwork@netcom.com (Steven L. Work) writes:
> : In article <3fopac$n63@news.iastate.edu>
> :            dickw@iastate.edu "Richard Wallingford" writes:
> : > Does anybody have ... an arbitrary length FFT?
>
> Actually, an FFT can be done on any composite length sequence....
> It's just that power-of-two sequences are the most efficient.

Are you sure?  There is a certain equivalence between computation of Fourier
and Cosine Transforms and ...

In <"Mixed-Radix Discrete Cosine Transform", _IEEE_Trans_Sig_Proc_ XLI-11
	(Nov '93)> Y.H. Chan and W.C. Siu write:
> ... our proposed radix-6 algorithm requires the least computational
> complexity among three algorithms whether the number of multiplications or
> additions per point is concerned.  In fact, when N is sufficiently large,
> the radix-2 algorithm becomes more efficient than the radix-6 algorithm.
> However, this virtual breakeven point occurs at N ~ 1.69*10^13 ....

I guess Mr. Wallingford might have a transform block this large but it
seems unlikely.
