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On robust signal reconstruction in noisy filter banks

Vikalo, Haris and Hassibi, Babak and Erdogan, Alper T. (2005) On robust signal reconstruction in noisy filter banks. Signal Processing, 85 (1). pp. 1-14. ISSN 0165-1684. doi:10.1016/j.sigpro.2004.08.011.

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We study the design of synthesis filters in noisy filter bank systems using an H∞ estimation point of view. The H∞ approach is most promising in situations where the statistical properties of the disturbances (arising from quantization, compression, etc.) in each subband of the filter bank is unknown, or is too difficult to model and analyze. For the important special case of unitary analysis polyphase matrices we obtain an explicit expression for the minimum achievable disturbance attenuation. For arbitrary analysis polyphase matrices, standard state-space H∞ techniques can be employed to obtain numerical solutions. When the synthesis filters are restricted to being FIR, as is often the case in practice, the design can be cast as a finite-dimensional semi-definite program. In this case, we can effectively exploit the inherent non-uniqueness of the H∞ solution to optimize for an additional criteria. By optimizing for average performance in addition to the H∞ criteria, we obtain mixed H^2/H∞ optimal FIR synthesis filters. Alternatively, if the additional criteria is concerned with penalizing occasional occurrence of large values of reconstruction errors more than frequent occurrence of small to moderate ones, we obtain risk-sensitive FIR synthesis filters. Numerical examples and comparisons with existing methods are also included.

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Additional Information:© 2004 Elsevier. Received 25 April 2002, Available online 17 September 2004.
Subject Keywords:Noisy filter banks; Robust signal reconstruction; H∞ design
Issue or Number:1
Record Number:CaltechAUTHORS:20150210-072703948
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54624
Deposited By: Shirley Slattery
Deposited On:11 Feb 2015 00:45
Last Modified:10 Nov 2021 20:36

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