A vector implementation of the Fast Fourier Transform algorithm

Author:
Bengt Fornberg

Journal:
Math. Comp. **36** (1981), 189-191

MSC:
Primary 68A10; Secondary 42A68

DOI:
https://doi.org/10.1090/S0025-5718-81-99783-0

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Abstract: A recent article in this journal by D. G. Korn and J. J. Lambiotte, Jr. discusses implementations of the FFT algorithm on the CDC STAR-100 vector computer. The 'Pease'-algorithm is recommended in cases when only a few transforms can be performed simultaneously. We show how the use of a different algorithm and of trigonometric tables will lead to more than three times faster execution times. The times for large transforms increase only about 39

**[1]**D. G. Korn & J. J. Lambiotte, Jr., "Computing the Fast Fourier Transform on a vector computer,"*Math. Comp.*, v. 33, 1979, pp. 977-992. MR**528051 (80k:65108)****[2]**J. W. Cooley & J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series,"*Math. Comp.*, v. 19, 1965, pp. 297-301. MR**0178586 (31:2843)****[3]**W. T. Cochran et al., "What is the Fast Fourier Transform?,"*IEEE Trans. Audio Electroacoust.*, v. Au-15, 1967, pp. 45-55.**[4]**M. C. Pease, "An adaption of the Fast Fourier Transform for parallel processing,"*J. Assoc. Comput. Mach.*, v. 15, 1968, pp. 253-264.**[5]**J. A. Glassman, "A generalization of the Fast Fourier Transform,"*IEEE Trans. Comput.*, v. C-19, 1970, pp. 106-116. MR**0253590 (40:6804)****[6]**S. Winograd, "On computing the discrete Fourier transform,"*Proc. Nat. Acad. Sci. U.S.A.*, v. 74, 1976, pp. 1005-1006. MR**0415993 (54:4070)**

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DOI:
https://doi.org/10.1090/S0025-5718-81-99783-0

Article copyright:
© Copyright 1981
American Mathematical Society