On computing the split-radix FFT

This paper presents an efficient Fortran program that computes the Duhamel-Hollmann split-radix FFT. An indexing scheme is used that gives a three-loop structure for the split-radix FFT that is very similar to the conventional Cooley-Tukey FFT. Both a decimation-in-frequency and a decimation-in-time program are presented. An arithmetic analysis is made to compare the operation count of the Cooley-Tukey FFT fo several different radixes to that of the split-radix FFT. The split-radix FFT seems to require the least total arithmetic of any power-of-two DFT algorithm.

[1]  C. Burrus,et al.  An in-place, in-order prime factor FFT algorithm , 1981 .

[2]  S. Winograd.  On computing the Discrete Fourier Transform. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Pierre Duhamel,et al.  Implementation of "Split-radix" FFT algorithms for complex, real, and real-symmetric data , 1986, IEEE Trans. Acoust. Speech Signal Process..

[4]  Douglas L. Jones,et al.  On computing the discrete Hartley transform , 1985, IEEE Trans. Acoust. Speech Signal Process..

[5]  S. Winograd.  Arithmetic complexity of computations , 1980 .

[6]  S. Winograd.  On the multiplicative complexity of the Discrete Fourier Transform , 1979 .

[7]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[8]  Henk D. L. Hollmann,et al.  Implementation of "Split-radix" FFT algorithms for complex, real, and real symmetric data , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  Pierre Duhamel,et al.  Existence of a 2n FFT algorithm with a number of multiplications lower than 2n+1 , 1984 .

[10]  J. Martens.  Recursive cyclotomic factorization--A new algorithm for calculating the discrete Fourier transform , 1984 .

[11]  R. Yavne,et al.  An economical method for calculating the discrete Fourier transform , 1899, AFIPS Fall Joint Computing Conference.

[12]  M. Vetterli,et al.  Simple FFT and DCT algorithms with reduced number of operations , 1984 .

[13]  P. Duhamel,et al.  `Split radix' FFT algorithm , 1984 .

[14]  M. Heideman,et al.  Multiply/Add tradeoffs in length-2nFFT algorithms , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.