Novel Short-Time Fractional Fourier Transform: Theory, Implementation, and Applications

Abstract

As a generalization of the classical Fourier transform (FT), the fractional Fourier transform (FRFT) has proven to be a powerful tool for signal processing and analysis. However, it is not suitable for processing signals whose fractional frequencies vary with time due to a lack of time localization information. A simple method to overcome this limitation is the short-time FRFT (STFRFT). There exist several different definitions of the STFRFT in the literature. Unfortunately, these existing definitions do not well generalize the classical result of the conventional short-time FT (STFT), which can be interpreted as a bank of FT-domain filters. The objective of this paper is to propose a novel STFRFT that preserves the properties of the conventional STFT and can be implemented easily in terms of FRFT-domain filter banks. We first present the novel STFRFT and then derive its inverse transform and basic properties. The time-fractional-frequency analysis of this transform is also presented. Moreover, the implementation of the proposed STFRFT is discussed. Finally, we provide several applications for the proposed STFRFT.