Real orthogonal polynomials in frequency analysis
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Coadvisor
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Undergraduate course
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Publisher
Amer Mathematical Soc
Type
Article
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Acesso aberto
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Abstract
We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than the Levinson algorithm, for the determination of the reflection coefficients of the corresponding real Szego polynomials from the given moments.
Description
Keywords
frequency analysis problem, frequency estimation, Orthogonal polynomials, Szego polynomials, para-orthogonal polynomials, quadrature
Language
English
Citation
Mathematics of Computation. Providence: Amer Mathematical Soc, v. 74, n. 249, p. 341-362, 2004.
