# Good-Thomas PFA

Chapter

## Abstract

The additive FFT algorithms of the preceding two chapters make no explicit use of the multiplicative structure of the indexing set. We will see how the multiplicative structure can be applied, in the case of transform size *N* = *RS*, where *R* and *S* are relatively prime, to design an FT algorithm that is similar in structure to these additive algorithms but no longer requires the twiddle factor multiplication. The idea is due to Good [2] in 1958 and Thomas [8] in 1963, and the resulting algorithm is called the Good-Thomas Prime Factor algorithm (PFA).

## Keywords

Discrete Fourier Transform Permutation Matrix Index Point Permutation Matrice Multiplicative Structure
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## References

- [1]Burrus, C. S. and Eschenbacher, P. W. “An In-place In-order Prime Factor FFT Algorithm”,
*IEEE Trans. Acoust., Speech and Signal Proc*,**29**, 1981, pp. 806–817.MATHCrossRefGoogle Scholar - [2]Good, I. J. “The Interaction Algorithm and Practical Fourier Analysis”,
*J. Royal Statist. Soc, Ser*.**B20**, 1958, pp. 361–375.MathSciNetGoogle Scholar - [3]Kolba, D. P. and Parks, T. W. “A Prime Factor FFT Algorithm Using high-speed Convolution”,
*IEEE Trans. Acoust., Speech and Signal Proc*.,**25**, 1977.Google Scholar - [4]Temperton, C. “A Note on Prime Factor FFT Algorithms”,
*J. Comput. Phys*.,**52**, 1983, pp. 198–204.MATHCrossRefGoogle Scholar - [5]Temperton, C. “A New Set of Minimum-add Small-n Rotated DFT Modules”, to appear in
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*Parallel Computing*. Google Scholar - [7]Temperton, C. “A Self-Sorting In-place Prime Factor Real/half-complex FFT Algorithm”, to appear in
*J. Comput. Phys*. Google Scholar - [8]Thomas, L. H. “Using a Computer to Solve Problems in Physics”, in
*Applications of Digital Computers*, Ginn and Co., 1963.Google Scholar - [9]Chu, S. and Burrus, C. S. “A Prime Factor FFT Algorithm Using Distributed Arithmetic”,
*IEEE Trans. Acoust., Speech and Signal Proc*.,**30**(2), April 1982, pp. 217–227.MathSciNetMATHCrossRefGoogle Scholar

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