Optimization of Synthesis Oversampled Complex Filter Banks

Abstract : An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an inverse FIR synthesis system. We also provide a method to ensure the Hermitian symmetry property on the synthesis side, which is serviceable to processing real-valued signals. As an invertible analysis scheme corresponds to a redundant decomposition, there is no unique inverse FB. Given a particular solution, we parameterize the whole family of inverses through a null space projection. The resulting reduced parameter set simplifies design procedures, since the perfect reconstruction constrained optimization problem is recast as an unconstrained optimization problem. The design of optimized synthesis FBs based on time or frequency localization criteria is then investigated, using a simple yet efficient gradient algorithm.
Document type :
Journal articles
IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2009, 57 (10), pp.3827 - 3843. 〈10.1109/TSP.2009.2023947〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00405293
Contributor : Jérôme Gauthier <>
Submitted on : Monday, July 20, 2009 - 11:21:14 AM
Last modification on : Saturday, March 18, 2017 - 1:03:42 AM
Document(s) archivé(s) le : Tuesday, June 15, 2010 - 8:31:16 PM

File

jg_2008pp_tsp_arxiv.pdf
Files produced by the author(s)

Identifiers

Citation

Jérôme Gauthier, Laurent Duval, Jean-Christophe Pesquet. Optimization of Synthesis Oversampled Complex Filter Banks. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2009, 57 (10), pp.3827 - 3843. 〈10.1109/TSP.2009.2023947〉. 〈hal-00405293〉

Share

Metrics

Record views

661

Document downloads

132