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An introduction to programming the Winograd Fourier transform algorithm (WFTA)

H.F. Silverman

Abstract

Recently, Dr. Shmuel Winograd discovered a new approach to the computation of the discrete Fourier transform (DFT). Relative to fast Fourier transform (FFT), the Winograd Fourier transform algorithm (WFTA) significantly reduces the number of multiplication operations; it does not increase the number of addition operations in many cases. This paper introduces the new algorithm and discusses the operations comparison problem. A guide for programming is included, as are some preliminary running times.

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Available abstract

Key concepts: Prime-factor FFT algorithm, Fast Fourier transform, Split-radix FFT algorithm, Discrete Fourier transform (general), Cyclotomic fast Fourier transform, Algorithm, Rader's FFT algorithm, Fourier transform