TITLE:
A Rational Approximation of the Fourier Transform by Integration with Exponential Decay Multiplier
AUTHORS:
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal, Brendan M. Quine
KEYWORDS:
Rational Approximation, Fourier Transform, Sampling, Sinc Function
JOURNAL NAME:
Applied Mathematics,
Vol.12 No.11,
November
18,
2021
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.