A Discrete Fractional Gabor Expansion for Time–Frequency Signal Analysis

In this work, we present a discrete fractional Gabor representation on a general, non-rectangular timefrequency lattice. The traditional Gabor expansion represents a signal in terms of time and frequency shifted basis functions, called Gabor logons. This constant-bandwidth analysis uses a fixed, and rectangular time-frequency plane tiling. Many of the practical signals require a more flexible, non-rectangular time-frequency lattice for a compact representation. The proposed fractional Gabor method uses a set of basis functions that are related to the fractional Fourier basis and generate a non-rectangular tiling. Simulation results are presented to illustrate the performance of our method. Key-Words: Time-frequency analysis, Gabor expansion, Fractional Fourier Transform.