Bound ratio minimization of filter bank frames

Authors:
Li Chai;Jingxin Zhang;Cishen Zhang;Edoardo Mosca
Affiliations:
Engineering Research Center of Metallurgical Automation and Measurement Technology, Wuhan University of Science and Technology, Wuhan, China;Department of Electrical and Computer Systems Engineering, Monash University, VIC, Australia;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;Dipartimento di Sistemi e Informatica, Universityá di Firenze, Firenze, Italy
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

This paper investigates and solves the problem of frame bound ratio minimization for oversampled perfect reconstruction (PR) filter banks (FBs). For a given analysis PRFB, a finite dimensional convex optimization algorithm is derived to redesign the subband gain of each channel. The redesign minimizes the frame bound ratio of the FB while maintaining its original properties and performance. The obtained solution is precise without involving frequency domain approximation and can be applied to many practical problems in signal processing. The optimal solution is applied to subband noise suppression and tree structured FB gain optimization, resulting in deeper insights andnovel solutions to these two general classes of problems and considerable performance improvement. Effectiveness of the optimal solution is demonstrated by extensive numerical examples.