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From: shep@datacube.UUCP
Newsgroups: net.graphics
Subject: Re: Re: FFT of image in sections ?
Message-ID: <6700028@datacube.UUCP>
Date: Wed, 14-Aug-85 09:22:00 EDT
Article-I.D.: datacube.6700028
Posted: Wed Aug 14 09:22:00 1985
Date-Received: Fri, 23-Aug-85 23:55:19 EDT
References: <208@mplvax.UUCP>
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Nf-ID: #R:mplvax:-20800:datacube:6700028:000:1390
Nf-From: datacube!shep    Aug 14 09:22:00 1985


In article <360@ur-laser.uucp> nitin@ur-laser.uucp (Nitin Sampat) writes:
>We know that processing small images takes less time.  Well, how does 
>one go about breaking up a large image and process it in sections,
>and then most importantly, how does one put all these sections back 
>to get the FFT of the original image ?

And carl lowenstein	sdcsvax!mplvax!cdl writes:
>Just a little philosophical fuel on the fire:  The whole idea behind the
>FFT (what makes it *F*ast) is that breaking a large dataset into sections,
>processing the sections, and then recombining them is faster than processing
>the whole thing all at once. (recursively, down to sections of size 2 or 4).

Exactly! It is the representation of a one-dimensional string of numbers
as a two-dimensional array that allows it to fall together. Two-dimensional
image transforms are handled as the linear combination of two one-dimensional
passes. (The DFT is separable.)

Radix-2 and radix-4 butterflies are common only because of their ease of use
on sequence lengths that are highly composite (i.e. powers of two). A
radix-5 butterfly might be used for performing a 60 point FFT algorithm.

Rabiner and Gold give a good discussion of this in their EE classic
"Theory and Application of DSP".

Shep Siegel                           UUCP: ihnp4!datacube!shep
Datacube Inc.; 4 Dearborn Rd.; Peabody, Ma. 01960; 617-535-6644