Wavelet Factorization and Related Polynomials

Our goal is exploring and better understanding factorizations of polyphase matrices for finite impulse response (FIR) filters. In particular, we focus on nearest neighbor factorizations discussed by Wickerhauser and Zhu that allow for efficient implementation of the discrete wavelet transform (DWT) for the algorithms of Daubechies and Sweldens and Mallat. Nearest neighbor lifting is a specific form of the general lifting scheme that improves the lifting algorithm by optimizing the number of efficient memory accesses. Nearest neighbor lifting factorizations are typically generated by implementing the Euclidean algorithm for Laurent polynomials, which introduces multiple choices of factorizations of a polyphase matrix associated with a filter, and are the main focus of this work.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2015

Author dc:creator

• Meyer, David

Contributors dc:contributor

• Victor Wickerhauser
• Victor Wickerhauser, Guido Weiss, Edward Willson, Robert Pless, Peter Luthy

• Daubechies
• Filter Bank
• Lifting Scheme
• Normality Abnormality
• Polynomial Remainder Sequence
• Wavelet
• Mathematics

Statement dc:rights

• I have not registered my thesis with the U.S. Copyright Office, and do not intend to.

Language dc:language

English (en)

Identifier

https://openscholarship.wustl.edu/art_sci_etds/492

OAI identifier oai:identifier

oai:openscholarship.wustl.edu:art_sci_etds-1492