On the Number of Multiplications Necessary to Compute a Length-2n DFT

IEEE Transactions on Acoustics, Speech, and Signal Processing

Volumn 34, Issue 1, 1986, Pages 91-95

  Heideman, Michael T ^a   Burrus, C Sidney ^a  

^a RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TRANSFORMATIONS - FAST FOURIER TRANSFORMS;

MULTIPLICATIONS; MULTIPLICATIVE COMPLEXITY;

SIGNAL PROCESSING;

EID: 0022667883     PISSN: 00963518     EISSN: None     Source Type: Journal    
DOI: 10.1109/TASSP.1986.1164785     Document Type: Article

References (23)

1. J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput., vol. 19, pp. 297–301, Apr. 1965.
2. G. D. Bergland, “A fast Fourier transform algorithm using base 8 iterations,” Math. Comput., vol. 22, pp. 275–279, Apr. 1968.
3. R. Yavne, “An economical method for calculating the discrete Fourier transform,” in Fall Joint Comput. Conf., AFIPS Conf. Proc., vol. 33, part 1, Spartan, Washington, DC, 1968, pp. 115–125.
4. P. Duhamel and H. Hollmann, “‘Split radix’ FFT algorithm,” Elec tron. Lett., vol. 20, pp. 14–16, Jan. 5, 1984.
5. C. M. Rader and N. M. Brenner, “A new principle for fast Fourier transformation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-24, pp. 264–266, June 1976.
6. K. M. Cho and G. C. Temes, “Real-factor FFT algorithms,” in Conf. Record 1978 IEEE Int. Conf. Acoust., Speech, Signal Processing, Tulsa, OK, Apr. 10–12, 1978, pp. 634–637.
7. G. Bruun, “z-transform DFT filters and FFT's,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-26, pp. 56–63, Feb. 1978.
8. R. D. Preuss, “Very fast computation of the radix-2 discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-30, pp. 595–607, Aug. 1982.
9. M. Vetterli and H. J. Nussbaumer, “Simple FFT and DCT algorithms with reduced number of operations,” Signal Processing, vol. 6, pp. 267–278, Aug. 1984.
10. J.-B. Martens, “Recursive cyclotomic factorization—A new algorithm for calculating the discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 750–761, Aug. 1984.
11. S. Winograd, “On computing the discrete Fourier transform,” Proc. Nat. Acad. Sci. USA, vol. 73, pp. 1005–1006, Apr. 1976.
12. —, “On computing the discrete Fourier transform,” Math. Comput., vol. 32, pp. 175–199, Jan. 1978.
13. —, “On the multiplicative complexity of the discrete Fourier transform,” Advances Math., vol. 32, pp. 83–117, May 1979.
14. —, “Signal processing and complexity of computation,” in Proc. 1980 IEEE Int. Conf. Acoust., Speech, Signal Processing, Denver, CO, Apr. 9–11, 1980, pp. 94–101.
15. —, “Application of complexity of computations to signal processing,” in Digital Image Processing, J. C. Simon and R. M. Haralick, Eds. Reidel: Dordrecht, 1981, pp. 1–17.
16. B. Mescheder, “On the number of active *-operations needed to compute the discrete Fourier transform,” Acta Informatica, vol. 13, pp. 383–408, May 1980.
17. P. Duhamel and H. Hollmann, “Existence of a 2 n FFT algorithm with a number of multiplications lower than 2 n + 1,” Electron. Lett., vol. 20, pp. 690–692, Aug. 16, 1984.
18. I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers. New York: Wiley, 1980.
19. S. Winograd, Arithmetic Complexity of Computations. Philadelphia, PA: SIAM Publications, 1980.
20. —, “On multiplication of polynomials modulo a polynomial,” SIAM J. Comput., vol. 9, pp. 225–229, May 1980.
21. L. Auslander and S. Winograd, “The multiplicative complexity of certain semilinear systems defined by polynomials,” Adv. Appl. Math., vol. 1, no. 3, pp. 257-299, 1980.
22. H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms. Berlin: Springer-Verlag, 1981.
23. L. Auslander, E. Feig, and S. Winograd, “The multiplicative complexity of the discrete Fourier transform,” Adv. Appl. Math., vol. 5, pp. 87-109, Mar. 1984.