On computing the discrete Fourier transform

Author:
S. Winograd

Journal:
Math. Comp. **32** (1978), 175-199

MSC:
Primary 68A10

DOI:
https://doi.org/10.1090/S0025-5718-1978-0468306-4

MathSciNet review:
0468306

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Abstract: A new algorithm for computing the Discrete Fourier Transform is described. The algorithm is based on a recent result in complexity theory which enables us to derive efficient algorithms for convolution. These algorithms are then used to obtain the new Discrete Fourier Transform algorithm.

**[1]**S. WINOGRAD, "Some bilinear forms whose multiplicative complexity depends on the field of constants," to be published in*Mathematical Systems Theory*, Vol. 10.**[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]**C. M. FIDUCCIA & Y. ZALCSTEIN,*Algebras Having Linear Multiplicative Complexities*, Technical Report 46, Dept. of Computer Science, State University of New York, Stony Brook, August 1975.**[4]**A. L. TOOM, "The complexity of a scheme of functional elements simulating the multiplication of integers,"*Dokl. Akad. Nauk SSSR*, v. 150, 1963, pp. 496-498 =*Soviet Math. Dokl.*, v. 4, 1963, pp. 714-716. MR**0156494 (27:6417)****[5]**C. M. RADER, "Discrete Fourier transforms when the number of data samples is prime,"*Proc. IEEE*, v. 5, no. 6, June 1968, pp. 1107-1108.**[6]**I. J. GOOD, "The interaction of algorithm and practical Fourier series,"*J. Roy. Statist. Soc. Ser. B*, v. 20, 1958, pp. 361-372; Addendum, v. 22, 1960, pp. 372-375. MR**0102888 (21:1674)**

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0468306-4

Article copyright:
© Copyright 1978
American Mathematical Society