A CLOSED-FORM DISCRETE FRACTIONAL GABOR EXPANSION

Abstract

We present a discrete fractional Gabor expansion based on the closed form discrete fractional Fourier transform. The traditional Gabor expansion represents a signal as a linear combination of time and frequency shifted basis functions. This constant-bandwidth analysis generates a rectangular time-frequency lattice which might lead to poor time-frequency localization for many signals. Proposed expansion uses a set of basis functions related to the fractional Fourier basis and generate a parallelogram-shaped tiling. Completeness and biorthogonality conditions of the new expansion are given.