A fractional Gabor expansion

Abstract

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.