Real orthogonal polynomials in frequency analysis

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 a...

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Detalles Bibliográficos
Autores: Bracciali, Cleonice Fátima [UNESP], Li, X, Ranga, A. S.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2004
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/21707
Acceso en línea:http://dx.doi.org/10.1090/S0025-5718-04-01672-2
http://hdl.handle.net/11449/21707
Access Level:acceso abierto
Palabra clave:frequency analysis problem
frequency estimation
Orthogonal polynomials
Szego polynomials
para-orthogonal polynomials
quadrature
Descripción
Sumario: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.