Fractional Fourier transform: a survey

Abstract

The Fractional Fourier transform (FRFT), which provides generalization of conventional Fourier Transform was introduced many years ago in mathematics literature by Namias. In this paper, definition, properties of fractional Fourier transform and its relationship with other transforms is discussed. Various definitions of discrete version of FRFT and their comparison is presented. FRFT falls under the category of Linear time frequency representations. Some of the applications of FRFT such as detection of signals in noise, image compression, reduction of side lobe levels using convolutional windows, and time-frequency analysis are illustrated with examples. It has been observed that FRFT can be used in more effective manner compared to Fourier transform with additional degrees of freedom.