Real orthogonal polynomials in frequency analysis

Detalhes bibliográficos
Autor(a) principal: Bracciali, Cleonice Fátima [UNESP]
Data de Publicação: 2004
Outros Autores: Li, X, Ranga, A. S.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
DOI: 10.1090/S0025-5718-04-01672-2
Texto Completo: http://dx.doi.org/10.1090/S0025-5718-04-01672-2
http://hdl.handle.net/11449/21707
Resumo: 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.
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spelling Real orthogonal polynomials in frequency analysisfrequency analysis problemfrequency estimationOrthogonal polynomialsSzego polynomialspara-orthogonal polynomialsquadratureWe 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.Univ Estadual Paulista, IBILCE, Dept Ciências Computacao & Estatist, BR-15054000 São Paulo, BrazilUniv Cent Florida, Dept Math, Orlando, FL 32816 USAUniv Estadual Paulista, IBILCE, Dept Ciências Computacao & Estatist, BR-15054000 São Paulo, BrazilAmer Mathematical SocUniversidade Estadual Paulista (Unesp)Univ Cent FloridaBracciali, Cleonice Fátima [UNESP]Li, XRanga, A. S.2014-05-20T14:01:31Z2014-05-20T14:01:31Z2004-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article341-362http://dx.doi.org/10.1090/S0025-5718-04-01672-2Mathematics of Computation. Providence: Amer Mathematical Soc, v. 74, n. 249, p. 341-362, 2004.0025-5718http://hdl.handle.net/11449/2170710.1090/S0025-5718-04-01672-2WOS:000224383800016830032245262246735871233097456100000-0002-6823-4204Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMathematics of Computation1.7501,939info:eu-repo/semantics/openAccess2022-02-09T12:29:30Zoai:repositorio.unesp.br:11449/21707Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:31:09.755069Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Real orthogonal polynomials in frequency analysis
title Real orthogonal polynomials in frequency analysis
spellingShingle Real orthogonal polynomials in frequency analysis
Real orthogonal polynomials in frequency analysis
Bracciali, Cleonice Fátima [UNESP]
frequency analysis problem
frequency estimation
Orthogonal polynomials
Szego polynomials
para-orthogonal polynomials
quadrature
Bracciali, Cleonice Fátima [UNESP]
frequency analysis problem
frequency estimation
Orthogonal polynomials
Szego polynomials
para-orthogonal polynomials
quadrature
title_short Real orthogonal polynomials in frequency analysis
title_full Real orthogonal polynomials in frequency analysis
title_fullStr Real orthogonal polynomials in frequency analysis
Real orthogonal polynomials in frequency analysis
title_full_unstemmed Real orthogonal polynomials in frequency analysis
Real orthogonal polynomials in frequency analysis
title_sort Real orthogonal polynomials in frequency analysis
author Bracciali, Cleonice Fátima [UNESP]
author_facet Bracciali, Cleonice Fátima [UNESP]
Bracciali, Cleonice Fátima [UNESP]
Li, X
Ranga, A. S.
Li, X
Ranga, A. S.
author_role author
author2 Li, X
Ranga, A. S.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Univ Cent Florida
dc.contributor.author.fl_str_mv Bracciali, Cleonice Fátima [UNESP]
Li, X
Ranga, A. S.
dc.subject.por.fl_str_mv frequency analysis problem
frequency estimation
Orthogonal polynomials
Szego polynomials
para-orthogonal polynomials
quadrature
topic frequency analysis problem
frequency estimation
Orthogonal polynomials
Szego polynomials
para-orthogonal polynomials
quadrature
description 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.
publishDate 2004
dc.date.none.fl_str_mv 2004-01-01
2014-05-20T14:01:31Z
2014-05-20T14:01:31Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1090/S0025-5718-04-01672-2
Mathematics of Computation. Providence: Amer Mathematical Soc, v. 74, n. 249, p. 341-362, 2004.
0025-5718
http://hdl.handle.net/11449/21707
10.1090/S0025-5718-04-01672-2
WOS:000224383800016
8300322452622467
3587123309745610
0000-0002-6823-4204
url http://dx.doi.org/10.1090/S0025-5718-04-01672-2
http://hdl.handle.net/11449/21707
identifier_str_mv Mathematics of Computation. Providence: Amer Mathematical Soc, v. 74, n. 249, p. 341-362, 2004.
0025-5718
10.1090/S0025-5718-04-01672-2
WOS:000224383800016
8300322452622467
3587123309745610
0000-0002-6823-4204
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mathematics of Computation
1.750
1,939
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 341-362
dc.publisher.none.fl_str_mv Amer Mathematical Soc
publisher.none.fl_str_mv Amer Mathematical Soc
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1822182482820202496
dc.identifier.doi.none.fl_str_mv 10.1090/S0025-5718-04-01672-2

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