Wavelets and multirate filter banks : theory, structure, design, and applications

Wavelets and filter banks have revolutionized signal processing with their ability to process data at multiple temporal and spatial resolutions. Fundamentally, continuous-time wavelets are governed by discrete-time filter banks with properties such as perfect reconstruction, linear phase and regularity. In this thesis, we study multi-channel filter bank factorization and parameterization strategies, which facilitate designs with specified properties that are enforced by the actual factorization structure. For M-channel filter banks (M =/> 2), we develop a complete factorization, M-channel lifting factorization, using simple ladder-like structures as predictions between channels to provide robust and efficient implementation; perfect reconstruction is structurally enforced, even under finite precision arithmetic and quantization of lifting coefficients. With lifting, optimal low-complexity integer wavelet transforms can thus be designed using a simple and fast algorithm that incorporates prescribed limits on hardware operations for power-constrained environments. As filter bank regularity is important for a variety of reasons, an aspect of particular interest is the structural imposition of regularity onto factorizations based on the dyadic form uvt. We derive the corresponding structural conditions for regularity, for which M-channel lifting factorization provides an essential parameterization. As a result, we are able to design filter banks that are exactly regular and amenable to fast implementations with perfect reconstruction, regardless of the choice of free parameters and possible finite precision effects. Further constraining u = v ensures regular orthogonal filter banks,

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Chen, Ying-Jui, 1972-

Advisor dc:contributor.advisor

• Kevin S. Amaratunga.

• Civil and Environmental Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/30140

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/30140