Application of the fast Fourier transform to computation of Fourier integrals, Fourier series, and convolution integrals

Abstract

The fast Fourier transform is a computational procedure for calculating the finite Fourier transform of a time series. In this paper, the properties of the finite Fourier transform are related to commonly used integral transforms including the Fourier transform and convolution integrals. The relationship between the finite Fourier transform and Fourier series is also discussed.

Keywords

FAST FOURIER TRANSFORMS
FOURIER SERIES
CONVOLUTION
FOURIER TRANSFORMS
INTEGRAL EQUATIONS
FREQUENCY
DISCRETE FOURIER TRANSFORMS
NETWORK ADDRESS TRANSLATION
DISCRETE TRANSFORMS
HARMONIC ANALYSIS

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