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A. V. Oppenheim. Su, Guolong, Ph. D. Massachusetts Institute of Technology Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2013-11-18T19:16:23Z 2013-11-18T19:16:23Z 2013 2013 http://hdl.handle.net/1721.1/82383 862075420 Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013. Cataloged from PDF version of thesis. Includes bibliographical references (p. 107-109). Polynomial decomposition has attracted considerable attention in computational mathematics. In general, the field identifies polynomials f(x) and g(x) such that their composition f(g(x)) equals or approximates a given polynomial h(x). Despite potentially promising applications, polynomial decomposition has not been significantly utilized in signal processing. This thesis studies the sensitivities of polynomial composition and decomposition to explore their robustness in potential signal processing applications and develops effective polynomial decomposition algorithms to be applied in a signal processing context. First, we state the problems of sensitivity, exact decomposition, and approximate decomposition. After that, the sensitivities of the composition and decomposition operations are theoretically derived from the perspective of robustness. In particular, we present and validate an approach to decrease certain sensitivities by using equivalent compositions, and a practical rule for parameter selection is proposed to get to a point that is near the minimum of these sensitivities. Then, new algorithms are proposed for the exact decomposition problems, and simulations are performed to make comparison with existing approaches. Finally, existing and new algorithms for the approximate decomposition problems are presented and evaluated using numerical simulations. by Guolong Su. S.M. 113 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. Polynomial decomposition algorithms in signal processing Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="ba1156a0-1f2a-4d20-9919-39ee62a015b9"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Polynomial decomposition algorithms in signal processing</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2013</PublicationDate> <Authors> <Author> <DisplayName>Su, Guolong, Ph. D. Massachusetts Institute of Technology</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>Polynomial decomposition has attracted considerable attention in computational mathematics. In general, the field identifies polynomials f(x) and g(x) such that their composition f(g(x)) equals or approximates a given polynomial h(x). Despite potentially promising applications, polynomial decomposition has not been significantly utilized in signal processing. This thesis studies the sensitivities of polynomial composition and decomposition to explore their robustness in potential signal processing applications and develops effective polynomial decomposition algorithms to be applied in a signal processing context. First, we state the problems of sensitivity, exact decomposition, and approximate decomposition. After that, the sensitivities of the composition and decomposition operations are theoretically derived from the perspective of robustness. In particular, we present and validate an approach to decrease certain sensitivities by using equivalent compositions, and a practical rule for parameter selection is proposed to get to a point that is near the minimum of these sensitivities. Then, new algorithms are proposed for the exact decomposition problems, and simulations are performed to make comparison with existing approaches. Finally, existing and new algorithms for the approximate decomposition problems are presented and evaluated using numerical simulations.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>