Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
Jeremy Axelrod
TL;DR
This paper presents a method to approximate the continuous Fourier transform using the discrete Fourier transform, enabling faster computation via FFT algorithms and discussing its advantages and limitations.
Contribution
It introduces a novel approach to approximate the analytic Fourier transform through the DFT, with practical MATLAB implementations.
Findings
The method enables efficient approximation of the Fourier transform.
It discusses the accuracy and computational benefits of the approach.
Prototypical MATLAB codes demonstrate practical implementation.
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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Taxonomy
TopicsDigital Filter Design and Implementation · Numerical Methods and Algorithms · Model Reduction and Neural Networks