A closed-form formula for calculating the Fourier transform of time-limited signals

Abstract

A new method for calculating the Fourier transform of a function is developed. This method is based on the generalization of the jump formula which is used in calculating the Fourier series of periodic functions. The developed formula is a very user-friend and handy equation. Besides the application of developed routine for calculating the Fourier transform, it is very useful in evaluating the convergence rate of the Fourier transform of the functions. It is believed that the proposed relation will very soon be appeared in Engineering Mathematics text books and communities