An economical method for calculating the discrete Fourier transform

Authors:
R. Yavne
Affiliations:
Raytheon Company, Bedford, Massachusetts
Venue:
AFIPS '68 (Fall, part I) Proceedings of the December 9-11, 1968, fall joint computer conference, part I
Year:
1968

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Abstract

With the advent of digital computers it became possible to compute the Discrete Fourier Transform for a large number of input points in relatively reasonable times. However, for certain uses a demand developed to compute the Discrete Fourier Transform in a very short time or even in real time. Also, a demand developed for computing the Fourier Transform for a very large number of input points. These demands resulted in a requirement for computing the Fourier Transform in the fastest time possible. A very economical way for computing the Fourier Transform was developed a few years ago and is known as the Cooley-Tukey Algorithm. This article describes another algorithm for computing the Discrete Fourier Transform where the required number of additions and subtractions is the same as in the Cooley-Tukey Algorithm; but the required number of multiplications is only one half of that in the Cooley-Tukey Algorithm.