Keywords

Fourier analysis, Fourier transformations

Abstract

This paper illustrates Winograd's approach to computing the Discrete Fourier Transform (DFT). This new approach changes the DFT into a cyclic convolution of 2 sequences, and illustrates shortcuts for computing this cyclic convolution. This method is known to reduce the number of multiplies required to about 20% less than the number of multiplies used by the techniques of the Fast Fourier Transform. Three approaches are discussed, one for prime numbers, one for products of primes, and lastly one for powers of odd primes. For powers of 2 Winograd's algorithm is, in general, inefficient and best if it is not used. A computer simulation is illustrated for the 35 point transform and its execution time is compared with that of the Fast Fourier Transform algorithm for 32 points.

Notes

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Graduation Date

Spring 1979

Advisor

Bauer, Christian S.

Degree

Master of Science (M.S.)

College

College of Engineering

Degree Program

Operations Research

Format

PDF

Pages

ii, 106 pages

Language

English

Rights

Public Domain

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Identifier

DP0013247

Subjects

Fourier analysis, Fourier transformations

Collection (Linked data)

Retrospective Theses and Dissertations

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