{"id":{"repo_id":"wustl","oai_identifier":"oai:openscholarship.wustl.edu:art_sci_etds-1492"},"canonical_url":"https://search.dev.ndltd.org/etd/wustl/oai:openscholarship.wustl.edu:art_sci_etds-1492","repository":{"repo_id":"wustl","name":"Washington University in St. Louis","base_url":"https://openscholarship.wustl.edu/do/oai/"},"display":{"title":"Wavelet Factorization and Related Polynomials","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Meyer, David"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Victor Wickerhauser","Victor Wickerhauser, Guido Weiss, Edward Willson, Robert Pless, Peter Luthy"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-05-15T07:00:00Z","date_published":"2015-05-15T07:00:00Z","updated_at":"2026-07-24T06:12:08Z","subjects":["Daubechies","Filter Bank","Lifting Scheme","Normality Abnormality","Polynomial Remainder Sequence","Wavelet","Mathematics"],"languages":["English (en)"],"rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/art_sci_etds/492"],"render_values":[{"text":"https://openscholarship.wustl.edu/art_sci_etds/492","href":"https://openscholarship.wustl.edu/art_sci_etds/492","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.7936/K7ZG6QD3","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Victor Wickerhauser","Victor Wickerhauser, Guido Weiss, Edward Willson, Robert Pless, Peter Luthy"]},{"key":"dc:creator","label":"Author","values":["Meyer, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-09-26T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics","Graduate School of Arts and Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Daubechies","Filter Bank","Lifting Scheme","Normality Abnormality","Polynomial Remainder Sequence","Wavelet","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]},{"key":"dc:rights","label":"Dc Rights","values":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7936/K7ZG6QD3","https://openscholarship.wustl.edu/art_sci_etds/492"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Permanent URL: https://doi.org/10.7936/K7ZG6QD3"]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Wavelet Factorization and Related Polynomials"]}]}],"canonical_facts":{"dc:contributor":["Victor Wickerhauser","Victor Wickerhauser, Guido Weiss, Edward Willson, Robert Pless, Peter Luthy"],"dc:creator":["Meyer, David"],"dc:date.available":["2015-09-26T07:00:00Z"],"dc:description":["Permanent URL: https://doi.org/10.7936/K7ZG6QD3"],"dc:description.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."],"dc:identifier":["https://doi.org/10.7936/K7ZG6QD3","https://openscholarship.wustl.edu/art_sci_etds/492"],"dc:language":["English (en)"],"dc:rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"dc:subject":["Daubechies","Filter Bank","Lifting Scheme","Normality Abnormality","Polynomial Remainder Sequence","Wavelet","Mathematics"],"dc:title":["Wavelet Factorization and Related Polynomials"],"thesis:degree_discipline":["Mathematics","Graduate School of Arts and Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:12:08Z"}