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A New Hybrid Algorithm for Computing a Fast Discrete Fourier Transform

I.S. Reed, T. K. Truong

Open publisher page 1 citations

Abstract

For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.

About this research paper

What this paper is about

For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.

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Available abstract

For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.

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

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