Paper Info
Title
A parametric class of discrete Gabor expansions
Abstract
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
Year
DOI
Venue
1996
10.1109/78.485917
IEEE Transactions on Signal Processing
Keywords
Field
DocType
discrete gabor expansions,gabor structure,simulation results,infinite analysis sequence,signal processing,pseudoframe decompositions,analytical formula,analysis sequence,complex modulation,parametric formula,algebraic formula,parametric class,various signal processing problem,gabor analysis sequences,different gabor analysis sequence,sequences,algorithm,gabor expansion,discrete gabor expansion,pseudoframe decomposition,simple algebraic formula,various application,transforms,translation,infinite analysis sequences,algorithm design and analysis,generic algorithm,visual system,helium,system of equations,computer science,mathematics,constraint optimization
Hilbert space,Signal processing,Discretization,Mathematical optimization,Algebraic number,General algorithm,System of linear equations,Gabor wavelet,Parametric statistics,Mathematics
Journal
Volume
Issue
ISSN
44
2
1053-587X
Citations 
PageRank 
References 
8
2.06
9
Authors
2
Name
Order
Citations
PageRank
Shidong Li1175.07
D.M. Healy, Jr.282.06