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2015 Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames
Martin Ehler
J. Appl. Math. 2015: 1-12 (2015). DOI: 10.1155/2015/861563


We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the original filter bank are preserved. Unitary filter banks providing perfect reconstruction are induced by tight generalized frames, which enable signal decomposition using a set of linear operators. If, in addition, frame elements have equal norm, then the signal energy is spread through the various filter bank channels in some uniform fashion, which is often more suitable for further signal processing. We start with a given generalized frame whose elements allow for fast matrix vector multiplication, as, for instance, convolution operators, and compute a normalized tight frame, for which signal analysis and synthesis still preserve those fast algorithmic schemes.


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Martin Ehler. "Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames." J. Appl. Math. 2015 1 - 12, 2015.


Published: 2015
First available in Project Euclid: 17 August 2015

zbMATH: 07132084
MathSciNet: MR3366493
Digital Object Identifier: 10.1155/2015/861563

Rights: Copyright © 2015 Hindawi

Vol.2015 • 2015
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