Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

Preprint English OPEN
Axelrod, Jeremy (2015)
  • Subject: Mathematics - Numerical Analysis

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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