Optimization of Synthesis Oversampled Complex Filter Banks

Details Optimization of Synthesis Oversampled Complex Filter Banks Optimization of Synthesis Oversampled Complex Filter Banks

2009-07-21

arxiv.org/abs/0907.3654v1

IEEE Transactions on Signal Processing, October 2009, Volume 57, Issue 10, p. 3827-3843

Computer Science

Information Theory

Scientific paper

10.1109/TSP.2009.2023947

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.

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