On the Prediction of a Class of Wide-Sense Stationary Random Processes

Autores
Medina, Juan Miguel; Cernuschi Frias, Bruno
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that under suitable conditions, a multi-band wide sense stationary stochastic process can be linearly predicted at time with arbitrarily small error using past samples taken at uniform rate. This result generalizes previous similar results for band-limited signals. Moreover we prove that the prediction problem from uniform past samples is equivalent to a disjoint translates condition on the spectrum together with the divergence of a logarithmic integral. We also show that, for the band-limited case, under similar conditions, non uniform samples can be taken.
Fil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Cernuschi Frias, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Materia
Prediction
Stationary Random Processes
Statistical Signal Processing
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19423
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the Prediction of a Class of Wide-Sense Stationary Random ProcessesMedina, Juan MiguelCernuschi Frias, BrunoPredictionStationary Random ProcessesStatistical Signal Processinghttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2We prove that under suitable conditions, a multi-band wide sense stationary stochastic process can be linearly predicted at time with arbitrarily small error using past samples taken at uniform rate. This result generalizes previous similar results for band-limited signals. Moreover we prove that the prediction problem from uniform past samples is equivalent to a disjoint translates condition on the spectrum together with the divergence of a logarithmic integral. We also show that, for the band-limited case, under similar conditions, non uniform samples can be taken.Fil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Cernuschi Frias, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaInstitute of Electrical and Electronics Engineers2011-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19423Medina, Juan Miguel; Cernuschi Frias, Bruno; On the Prediction of a Class of Wide-Sense Stationary Random Processes; Institute of Electrical and Electronics Engineers; IEEE Transactions On Signal Processing; 59; 1; 1-2011; 70-771053-587XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://ieeexplore.ieee.org/document/5590307/info:eu-repo/semantics/altIdentifier/doi/10.1109/TSP.2010.2081984info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:41:29Zoai:ri.conicet.gov.ar:11336/19423instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:41:29.646CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the Prediction of a Class of Wide-Sense Stationary Random Processes
title On the Prediction of a Class of Wide-Sense Stationary Random Processes
spellingShingle On the Prediction of a Class of Wide-Sense Stationary Random Processes
Medina, Juan Miguel
Prediction
Stationary Random Processes
Statistical Signal Processing
title_short On the Prediction of a Class of Wide-Sense Stationary Random Processes
title_full On the Prediction of a Class of Wide-Sense Stationary Random Processes
title_fullStr On the Prediction of a Class of Wide-Sense Stationary Random Processes
title_full_unstemmed On the Prediction of a Class of Wide-Sense Stationary Random Processes
title_sort On the Prediction of a Class of Wide-Sense Stationary Random Processes
dc.creator.none.fl_str_mv Medina, Juan Miguel
Cernuschi Frias, Bruno
author Medina, Juan Miguel
author_facet Medina, Juan Miguel
Cernuschi Frias, Bruno
author_role author
author2 Cernuschi Frias, Bruno
author2_role author
dc.subject.none.fl_str_mv Prediction
Stationary Random Processes
Statistical Signal Processing
topic Prediction
Stationary Random Processes
Statistical Signal Processing
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv We prove that under suitable conditions, a multi-band wide sense stationary stochastic process can be linearly predicted at time with arbitrarily small error using past samples taken at uniform rate. This result generalizes previous similar results for band-limited signals. Moreover we prove that the prediction problem from uniform past samples is equivalent to a disjoint translates condition on the spectrum together with the divergence of a logarithmic integral. We also show that, for the band-limited case, under similar conditions, non uniform samples can be taken.
Fil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Cernuschi Frias, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
description We prove that under suitable conditions, a multi-band wide sense stationary stochastic process can be linearly predicted at time with arbitrarily small error using past samples taken at uniform rate. This result generalizes previous similar results for band-limited signals. Moreover we prove that the prediction problem from uniform past samples is equivalent to a disjoint translates condition on the spectrum together with the divergence of a logarithmic integral. We also show that, for the band-limited case, under similar conditions, non uniform samples can be taken.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/19423
Medina, Juan Miguel; Cernuschi Frias, Bruno; On the Prediction of a Class of Wide-Sense Stationary Random Processes; Institute of Electrical and Electronics Engineers; IEEE Transactions On Signal Processing; 59; 1; 1-2011; 70-77
1053-587X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19423
identifier_str_mv Medina, Juan Miguel; Cernuschi Frias, Bruno; On the Prediction of a Class of Wide-Sense Stationary Random Processes; Institute of Electrical and Electronics Engineers; IEEE Transactions On Signal Processing; 59; 1; 1-2011; 70-77
1053-587X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://ieeexplore.ieee.org/document/5590307/
info:eu-repo/semantics/altIdentifier/doi/10.1109/TSP.2010.2081984
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844614446091075584
score 13.070432

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