Wavelets and filter banks: New results and applications

Wavelet transforms provide a new technique for time-scale analysis of non-stationary signals. Wavelet analysis uses orthonormal bases in which computations can be done efficiently with multirate systems known as filter banks. This thesis develops a comprehensive set of tools for (multidimensional) multirate signal analysis and uses them to investigate two multirate systems: filter banks and transmultiplexers. Several results in filter bank theory are obtained: a new parameterization of unitary filter banks, a theory of modulated filter banks, a theory of filter banks with symmetry restrictions, reduction of the multidimensional rational sampling rate filter bank problem to the uniform sampling rate filter bank problem, solution to the completion problem for filter banks (by reducing it to the (YJBK) parameterization problem in control theory) etc. Perfect reconstruction filter banks are shown to give structured decompostions of separable Hilbert spaces. Filter banks are used to construct several classes of wavelet bases: multiplicity M wavelet tight frames and frames, regular multiplicity M orthonormal bases, modulated wavelet tight frames etc. The thesis describes the design of optimal wavelets for signal representation and the wavelet sampling theorem. Application of wavelets in signal interpolation and in the approximation of linear-translation invariant operators is investigated.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

1993

Author dc:creator

• Gopinath, Ramesh Ambat

Advisor dc:contributor.advisor

• Burrus, C. Sidney

• Electronics
• Electrical engineering
• Mathematics

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/16626

OAI identifier oai:identifier

oai:repository.rice.edu:1911/16626