# Good-Thomas PFA

Chapter

## Abstract

The additive FFT algorithms of the preceeding two chapters make no explicit use of the multiplicative structure of the indexing set. We will see how this multiplicative structure can be applied, in the case of transform size *N* = *RS*, where *R* and *S* are relatively prime, to design a FT algorithm, similar in structure to these additive algorithms, but no longer requiring 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., ASSP 29*, (1981), pp. 806–817.MATHCrossRefGoogle Scholar - [2]Good, I.J. “The Interaction Algorithm and Practical Fourier Analysis”,
*J. Royal Statist,’ oc, Ser.*B20 (1958):361–375.MathSciNetMATHGoogle Scholar - [3]Kolba, D.P. and Parks, T.W. “A Prime Factor FFT Algorithm Using high-speed Convolution”,
*IEEE Trans.*ASSP 25(1977).Google Scholar - [4]Temperton, C. “A Note on Prime Factor FFT Algorithms”,
*J. Comput. Physics.*, 52 (1983), PP. 198–204.MATHCrossRefGoogle Scholar - [5]Temperton, C. “A New Set of Minimum-add Small-n Rotated DFT Modules”, to appear in
*J. Comput. Physics*.Google Scholar - [6]Temperton, C. “Implementation of A Prime Factor FFT Algorithm on CRAY-1”, to appear in
*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., Boston, Mass., 1963.Google Scholar
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© Springer Science+Business Media New York 1989