Fourier transforms using Mathematica The Fourier transform is a ubiquitous tool used in most areas of engineering and physical sciences. The purposes of this book are two fold: (1) to introduce the reader to the properties of Fourier transforms and their uses and (2) to introduce the reader to the program Mathematica and demonstrate its use in Fourier analysis. Unlike many other introductory treatments of the Fourier transform this treatment will focus from the start on both one dimensional and two dimensional transforms the latter of which play an important role in optics and digital image processing as well as in many other applications. It is hoped that by the time the reader has completed this book he or she will have a basic understanding of Fourier analysis and Mathematica