A PARAMETRIC CLASS OF DISCRETE GABOR EXPANSIONS

A new approach to the study of the discrete Gabor expansion (DGE) is i ntroduced and analyzed in detail using the theory of pseudoframe decom positions (Section II). A parametric and analytical formula for a clas s of different Gabor analysis sequences is derived, It is a simple alg ebraic formula rather than another abstract system of equations. For t he first time, the structure of analysis sequences is questioned. We s how that while there is a class of infinite analysis sequences that po ssess the Gabor (translation and complex modulation) structure, there are also infinite analysis sequences of arbitrary forms. Simulation re sults are provided to demonstrate the proposed algorithms. The study o f the DGE by means of the theory of pseudoframe decompositions reveals a much broader mathematical perspective on the DGE. The general algor ithm derived provides a feasible platform for optimizations in discret e Gabor expansions arising from various applications. This is an area that can surely be exploited as algorithms of DGE's become known and a pplications become more and more intensive.