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RESEARCH PRODUCT
Efficient Analysis and Synthesis Using a New Factorization of the Gabor Frame Matrix
Wladimiro Diaz-villanuevaSalvador Moreno-picotMiguel Arevalillo-herráezFrancesc J. Ferrisubject
Signal processingCurrent (mathematics)Computer science020206 networking & telecommunicationsContext (language use)010103 numerical & computational mathematics02 engineering and technology01 natural sciencesTime–frequency analysisMatrix decompositionMatrix (mathematics)Operator (computer programming)FactorizationSignal Processing0202 electrical engineering electronic engineering information engineering0101 mathematicsElectrical and Electronic EngineeringAlgorithmdescription
In this paper, we consider the case in which one needs to carry out Gabor analysis and synthesis on large signals using a short support analysis window and its corresponding, possibly longer canonical dual window, respectively. In this asymmetric context, we propose a novel factorization of the Gabor frame operator that exploits its strong and well-known structure and leads to a computational cost for synthesis, which is comparable to the one needed for short support analysis. The proposed factorization applies to any Gabor system with very mild conditions and leads to a potentially promising alternative to current synthesis algorithms in the case of short analysis windows whose support is slightly above the number of frequency channels.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-09-01 | IEEE Transactions on Signal Processing |