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A fast DFT algorithm using complex integer transforms

I.S. Reed, T. K. Truong

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Abstract

Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.

About this research paper

What this paper is about

Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.

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Available abstract

Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.

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

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