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]**David G. Korn and Jules J. Lambiotte Jr.,*Computing the fast Fourier transform on a vector computer*, Math. Comp.**33**(1979), no. 147, 977–992. MR**528051**, https://doi.org/10.1090/S0025-5718-1979-0528051-4**[2]**James W. Cooley and John W. Tukey,*An algorithm for the machine calculation of complex Fourier series*, Math. Comp.**19**(1965), 297–301. MR**0178586**, https://doi.org/10.1090/S0025-5718-1965-0178586-1**[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. Computers**C-19**(1970), 105–116. MR**0253590****[6]**Shmuel Winograd,*On computing the discrete Fourier transform*, Proc. Nat. Acad. Sci. U.S.A.**73**(1976), no. 4, 1005–1006. MR**0415993**

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

Article copyright:
© Copyright 1981
American Mathematical Society