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).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Burrus, C.S. and Eschenbacher, P.W. “An In-place In-order Prime Factor FFT Algorithm”, IEEE Trans., ASSP 29, (1981), pp. 806–817.
Good, I.J. “The Interaction Algorithm and Practical Fourier Analysis”, J. Royal Statist,’ oc, Ser. B20 (1958):361–375.
Kolba, D.P. and Parks, T.W. “A Prime Factor FFT Algorithm Using high-speed Convolution”, IEEE Trans. ASSP 25(1977).
Temperton, C. “A Note on Prime Factor FFT Algorithms”, J. Comput. Physics., 52 (1983), PP. 198–204.
Temperton, C. “A New Set of Minimum-add Small-n Rotated DFT Modules”, to appear in J. Comput. Physics.
Temperton, C. “Implementation of A Prime Factor FFT Algorithm on CRAY-1”, to appear in Parallel Computing.
Temperton, C. “A Self-sorting In-place Prime Factor Real/half-complex FFT Algorithm”, to appear in J. Comput. Phys.
Thomas, L.H. “Using a Computer to Solve Problems in Physics”, in Applications of Digital Computers, Ginn and Co., Boston, Mass., 1963.
Chu, S. and Burrus, C.S. ”A Prime Factor FFT Algorithm Using Distributed Arithmetic”, IEEE Trans. on ASSP, Vol. 30, No. 2, pp. 217–227, April 1982.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tolimieri, R., An, M., Lu, C. (1989). Good-Thomas PFA. In: Burrus, C.S. (eds) Algorithms for Discrete Fourier Transform and Convolution. Signal Processing and Digital Filtering. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3854-4_5
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3854-4_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3856-8
Online ISBN: 978-1-4757-3854-4
eBook Packages: Springer Book Archive