Optimal noise reduction in oversampled PR filter banks

Authors:
Li Chai;Jingxin Zhang;Cishen Zhang;Edoardo Mosca
Affiliations:
Engineering Research Center of Metallurgical Automation and Measurement Technology, and the Key Lab of Metallurgical Equipment and Control, 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:
2009

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Abstract

This paper studies the optimal noise reduction problem for oversampled filter banks (FBs) with perfect reconstruction (PR) constraint. Both the optimal design and worst case design are considered, where the former caters for the noise with known power spectral density (PSD) and the latter for the noise with unknown PSD. State-space based explicit formulae involving only algebraic Riccati equation and matrix manipulations are provided for the general (IIR or FIR) oversampled PR FBs and the relations between different cases are analyzed and revealed. Extensive numerical examples are provided to illustrate the proposed design methods and to show their effectiveness.