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arXiv · 2001.07533

A rational approximation of the Fourier transform by integration with exponential decay multiplier

Sanjar M. Abrarov·Rehan Siddiqui·Rajinder K. Jagpal·Brendan M. Quine
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Abstract

Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from shifting property of the Fourier transform. In this work we show how to represent the Fourier transform of a function $f(t)$ in form of a ratio of two polynomials without any trigonometric multiplier. A MATLAB code showing algorithmic implementation of the proposed method for rational approximation of the Fourier transform is presented.

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Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal, Brendan M. Quine. 2022-10-16. A rational approximation of the Fourier transform by integration with exponential decay multiplier. https://doi.org/10.4236/am.2021.1211063

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