A fractional Gabor expansion

We present a fractional Gabor expansion on a non-rectangular time-frequency lattice. Sinusoidal analysis used in the traditional Gabor expansion is not appropriate for a compact representation for chirp-type signals. Basis functions of the proposed expansion are obtained via fractional Fourier basis. Completeness and biorthogonality conditions of the new expansion are derived. (C) 2003 The Franklin Institute. Published by Elsevier Ltd. All rights reserved

A fractional Gabor transform

We present a fractional Gabor expansion on a general, nonrectangular time-frequency lattice. The traditional Gabor expansion represents a signal in terms of time and frequency shifted basis functions, called Gabor logons. This constant bandwidth analysis results in a fixed, 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 expansion uses a set of basis functions that are related to the fractional Fourier basis and generate a non-rectangular tiling. The completeness and bi-orthogonality conditions of the new Gabor basis are discussed