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Published July 2003 | Published
Book Section - Chapter Open

On the least squares signal approximation model for overdecimated rational nonuniform filter banks and applications

Abstract

With the advent of wavelets for lossy data compression came the notion of representing signals in a certain vector space by their projections in well chosen subspaces of the original space. In this paper, we consider the subspace of signals generated by an overdecimated rational nonuniform filter bank and find the optimal conditions under which the mean-squared error between a given deterministic signal and its representation in this subspace is minimized for a fixed set of synthesis filters. Under these optimal conditions, it is shown that choosing the synthesis filters to further minimize this error is simply an energy compaction problem. With this, we introduce the notion of deterministic energy compaction filters for classes of signals. Simulation results are presented showing the merit of our proposed method for optimizing the synthesis filters.

Additional Information

© 2003 IEEE. Issue Date: 6-9 July 2003. Date of Current Version: 18 August 2003. Work supported in part by the ONR grant N00014-99-1-1002, USA.

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