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A Cooley-Tukey modified algorithm in fast Fourier transform

김화준|Somchai Lekcharoen
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2011.09|한국수학논문집 (Korean Journal of Mathematics)|제19권 제3호|pp. 243-253

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키워드

DFTFFTscalingCooley-Tukey algorithmminimal operation
주제분류수학

초록

We would like to propose a Cooley-Tukey modified algorithm in fast Fourier transform(FFT). Of course, this is a kind of Cooley-Tukey twiddle factor algorithm and we focused on the choice of integers. The proposed algorithm is better than existing ones in speeding up the calculation of the FFT.

Abstract

We would like to propose a Cooley-Tukey modified algorithm in fast Fourier transform(FFT). Of course, this is a kind of Cooley-Tukey twiddle factor algorithm and we focused on the choice of integers. The proposed algorithm is better than existing ones in speeding up the calculation of the FFT.

참고문헌 (13)

  1. G. Beylkin, "On the fast Fourier transform of functions with singularities", Appl. Comput. Harmon. Anal, 2, pp.363~381 (1995)
  2. E.O. Brigham, "The fast Fourier transform and its applications" (1988), Prentice-Hall International Inc. New Jersey
  3. E. Candes, "Fast computation of Fourier integral operators", Math. NA, 1, pp.1~31 (2006)
  4. P. Carr, "Option valuation using the fast Fourier transform", Journal of Computational Finance, 2(4), pp.1~8 (1999)
  5. J.W. Cooley, "An algorithm for the machine calculation of complex Fourier series", Math. Comp, 19(90), pp.297~301 (1965)
  6. M.E. Deisher, "Adaptive noise cancellation using fast optimum block algorithms", IEEE Int. Symposium on Circuits and Systems 1, pp.698~701 (1991)
  7. D.L. Jones, "A resolution comparison of several time-frequency representations", IEEE Trans. Signal Process, 40(2), pp.413~420 (1992)
  8. A. Oppenheim, "Computation of spectra with unequal resolution using the fast Fourier transform", Proc. IEEE, 59, pp.299~301 (1971)
  9. P. Duhamel, "Spilt-radix FFT algorithm", Electronics Letters, 20(1), pp.14~16 (1984)
  10. P. Duhamel, "Fast Fourier transforms: a tutorial review and a state of the art", Signal Processing, 19, pp.259~299 (1990)
  11. 이준엽, "Accelerating the nonuniform fast Fourier transform", SIAM REVIEW, 46(3), pp.443~454, SIAM PUBLICATIONS
  12. S. Winograd, "On computing the discrete Fourier transform", Math. Comp, 32(141), pp.175~199 (1978)
  13. X.G. Xia, "Discrete Chirp-Fourier transform and its application to Chirp rate estimation", IEEE Trans. Signal Process, 48(11), pp.3122~3133 (2000)

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