A parametric class of discrete Gabor expansions

The Gabor expansion and its discretization have been widely studied, and many potential applications have been suggested in various signal processing problems. A new approach to the study of the discrete Gabor expansion (DGE) is introduced and analyzed in detail using the theory of pseudoframe decompositions. A parametric and analytical formula for a class of different Gabor analysis sequences is derived. It is a simple algebraic formula rather than another abstract system of equations. For the first time, the structure of analysis sequences is questioned. We show that while there is a class of infinite analysis sequences that possess the Gabor (translation and complex modulation) structure, there are also infinite analysis sequences of arbitrary forms. Simulation results are provided to demonstrate the proposed algorithms. The study of the DGE by means of the theory of pseudoframe decompositions reveals a much broader mathematical perspective on the DGE. The general algorithm derived provides a feasible platform for optimizations in discrete Gabor expansions arising from various applications. This is an area that can surely be exploited as algorithms of DGEs become known and applications become more and more intensive