Fractional Fourier transform as a signal processing tool: An overview of recent developments

Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered many times over the past WO years. In this paper, we provide an overview of recent contributions pertaining to the FRFT. Specifically, the paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT. It discusses three major topics. First, the manuscripts relates the FRET to other mathematical transforms. Second, it discusses various approaches for practical realizations of the FRFT. Third, we overview the practical applications of the FRET. From these discussions, we can clearly state that the FRET is closely related to other mathematical transforms, such as time-frequency and linear canonical transforms. Nevertheless, we still feel that major contributions are expected in the field of the digital realizations and its applications, especially, since many digital realizations of the FRET still lack properties of the continuous FRET. Overall, the FRFT is a valuable signal processing tool. Its practical applications are expected to grow significantly in years to come, given that the FRET offers many advantages over the traditional Fourier analysis. (C) 2010 Elsevier B.V. All rights reserved.