Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

2015/08/06 by Axelrod, Jeremy
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1508.01282

Abstract

The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.

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