Polynomial decomposition algorithms in signal processing
Name
862075420-MIT.pdf
Description
Full printable version
Size
6.77 MB
Format
Adobe PDF
Checksum (MD5)
c60879425a89ec7ed9b50e4335d32535
Author(s)
Su, Guolong, Ph. D. Massachusetts Institute of Technology
Advisor(s)
A. V. Oppenheim.
Date Issued
2013
Publisher
Massachusetts Institute of Technology
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.
Description
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).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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