Abstract
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.
Committee Chair
Victor Wickerhauser
Committee Members
Victor Wickerhauser, Guido Weiss, Edward Willson, Robert Pless, Peter Luthy
Degree
Doctor of Philosophy (PhD)
Author's Department
Mathematics
Document Type
Dissertation
Date of Award
Spring 5-15-2015
Language
English (en)
DOI
https://doi.org/10.7936/K7ZG6QD3
Recommended Citation
Meyer, David, "Wavelet Factorization and Related Polynomials" (2015). Arts & Sciences Theses and Dissertations. 492.
The definitive version is available at https://doi.org/10.7936/K7ZG6QD3
Comments
Permanent URL: https://doi.org/10.7936/K7ZG6QD3