Split-radix algorithms for length-p/sup m/ DFTs

Reasons are suggested why the split-radix algorithm is better than any single-radix algorithm on length-2/sup m/ DFTs (discrete Fourier transforms). The split-radix approach is generalized to length-p/sup m/ DFTs. It is shown that whenever a radix-p/sup 2/ outperforms a radix-p algorithm, a radix-p/p/sup 2/ algorithm will outperform both of them. As an example, a radix-3/9 algorithm is developed for length-3/sup m/ DFTs.<<ETX>>

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

[2]  Douglas L. Jones,et al.  Real-valued fast Fourier transform algorithms , 1987, IEEE Trans. Acoust. Speech Signal Process..

[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]  R. Stasinski Easy generation of small-Ndiscrete Fourier transform algorithms , 1986 .

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

[6]  E. Dubois,et al.  A new algorithm for the radix-3 FFT , 1978 .

[7]  Martin Vetterli,et al.  Split-radix algorithms for length-pm DFT's , 1989, IEEE Trans. Acoust. Speech Signal Process..

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

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

[10]  C. Sidney Burrus,et al.  On computing the split-radix FFT , 1986, IEEE Trans. Acoust. Speech Signal Process..

[11]  C. Sidney Burrus,et al.  On the number of multiplications necessary to compute a length-2nDFT , 1986, IEEE Trans. Acoust. Speech Signal Process..

[12]  Irving John Good,et al.  The Interaction Algorithm and Practical Fourier Analysis , 1958 .

[13]  Ken'iti Kido,et al.  A new FFT algorithm of radix 3, 6, and 12 , 1986, IEEE Trans. Acoust. Speech Signal Process..

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