November 2010
Intermediate to advanced
288 pages
8h 34m
English
book
Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation
by C. Britton Rorabaugh
Content preview from Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation
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Note 19. FFT: Prime Factor Algorithm
The radix-2 algorithms described in Notes 17 and 18 are very useful, but in certain situations, a DFT block size of 2k is just not acceptable. The prime factor algorithm (PFA) is a technique for constructing fast transforms of length N, where N can be expressed as a product of mutually prime factors. A DFT of length N = N1N2 can be restructured as an N1 by N2 two-dimensional DFT:
19.1
where
W1 = exp(–j2p/N1)
W2 = exp(–j2p/N2)
In order to make use of the restructured transform, the one-dimensional input sequence, x[n], must be mapped into a two-dimensional sequence, x2[n1, n2], using the index transformation ...
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