Numerical Implementation of Fourier Transforms and Associated Problems

Abstract

Fourier transforms initially used for the solution of problems in mathematical physics has today become apowerful tool of data analysis in wide spectrum of disciplines ranging from electrical engineering to socialsciences. Its widespread applications can be attributed to the development of discrete Fourier transforms inmiddle part of the last century and subsequent development of fast Fourier transform algorithms which madeits numerical implementation possible using digital computers. This paper reviews the limitations of theFourier transform technique and associated problems and provide suggestions to overcome them.

KEYWORDS: Discrete Fourier transforms, Aliasing, High Frequency Instabilities, Truncation Errors,Symmetry Relationships