Issue No.06 - June (1981 vol.30)
I.S. Reed , Department of Electrical Engineering, University of Southern California
Recently,1 the authors proposed a hybrid algorithm for computing the discrete Fourier transform (DFT) of certain long transform lengths. In that technique, a Winograd-type algorithm was used in conjunction with the Mersenne prime-number theoretic transform to perform a DFT. Even though this technique requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm, it increases the number of additions considerably. In this letter it is proposed to use Winograd's algorithm for computing the Mersenne prime-number theoretic transform in the transform portion of the hybrid algorithm. It is shown that this can reduce significantly the number of additions while still maintaining about the same number of multiplications.
I.S. Reed, B. Benjauthrit, "Addendum to "A New Hybrid Algorithm for Computing a Fast Discrete Fourier Transform"", IEEE Transactions on Computers, vol.30, no. 6, pp. 453-454, June 1981, doi:10.1109/TC.1981.1675814