Optimization of synthesis oversampled complex filter banks

  • Authors:

  • Jérôme Gauthier;Laurent Duval;Jean-Christophe Pesquet

  • Affiliations:

  • Laboratoire d’Informatique Gaspard Monge CNRS-UMR 8049, Université Paris-Est, Marne-la-Vallée Cedex 2, France;Institut Français du Pétrole, IFP, Technology, Computer Science and Applied Mathematics Division, Rueil-Malmaison, France;Laboratoire d’Informatique Gaspard Monge CNRS-UMR 8049, Université Paris-Est, Marne-la-Vallée Cedex 2, France

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2009

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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 them investigated, using a simple yet efficient gradient algorithm.