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 AM  Vol.12 No.11 , November 2021
A Rational Approximation of the Fourier Transform by Integration with Exponential Decay Multiplier
Sanjar M. Abrarov1,2, Rehan Siddiqui2,3,4, Rajinder K. Jagpal3,4, Brendan M. Quine1,2,4
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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 the 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.
Keywords: Rational Approximation, Fourier Transform, Sampling, Sinc Function
Cite this paper: Abrarov, S. , Siddiqui, R. , Jagpal, R. and Quine, B. (2021) A Rational Approximation of the Fourier Transform by Integration with Exponential Decay Multiplier. Applied Mathematics, 12, 947-962. doi: 10.4236/am.2021.1211063.
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