Date of Award
Doctor of Philosophy (PhD)
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.
Chair and Committee
Victor Wickerhauser, Guido Weiss, Edward Willson, Robert Pless, Peter Luthy
Meyer, David, "Wavelet Factorization and Related Polynomials" (2015). Arts & Sciences Electronic Theses and Dissertations. 492.