The fractional fourier transform

A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are discussed. An overview of applications which have so far received interest are given and some potential application areas remaining to be explored are noted.

1 Introduction

The purpose of this paper is to provide a brief introduction to the fractional Fourier transform (FRT). Since the ordinary Fourier transform and related techniques are of importance in the control field, it is natural to expect the fractional Fourier transform to find many applications as well. This expectation. is further supported by the fact that the fractional Fourier transform has already found many applications in the areas of signal processing and communications. This paper will provide general motivation and mention some of the more important properties of the transform. Those interested in learning more are referred to a recent book on the subject [1] or the chapter-length treatment [2].