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

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.