An unconstrained optimization approach to empirical mode decomposition

Autores
Colominas, Marcelo Alejandro; Schlotthauer, Gaston; Torres, Maria Eugenia
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Empirical mode decomposition (EMD) is an adaptive (data-driven) method to decompose non-linear and non-stationary signals into AM-FM components. Despite its well-known usefulness, one of the major EMD drawbacks is its lack of mathematical foundation, being defined as an algorithm output. In this paper we present an alternative formulation for the EMD method, based on unconstrained optimization. Unlike previous optimization-based efforts, our approach is simple, with an analytic solution, and its algorithm can be easily implemented. By making no explicit use of envelopes to find the local mean, possible inherent problems of the original EMD formulation (such as the under- and overshoot) are avoided. Classical EMD experiments with artificial signals overlapped in both time and frequency are revisited, and comparisons with other optimization-based approaches to EMD are made, showing advantages for our proposal both in recovering known components and computational times. A voice signal is decomposed by our method evidencing some advantages in comparison with traditional EMD and noise-assisted versions. The new method here introduced catches most flavors of the original EMD but with a more solid mathematical framework, which could lead to explore analytical properties of this technique.
Fil: Colominas, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina
Fil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Entre Ríos. Universidad Nacional de Entre Ríos. Centro de Investigaciones y Transferencia de Entre Ríos; Argentina
Fil: Torres, Maria Eugenia. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Empirical Mode Decomposition (Emd)
Convex Optimization
Time Frequency
Data-Driven Methods
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:11336/41591
Acceder
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network_name_str CONICET Digital (CONICET)
spelling An unconstrained optimization approach to empirical mode decompositionColominas, Marcelo AlejandroSchlotthauer, GastonTorres, Maria EugeniaEmpirical Mode Decomposition (Emd)Convex OptimizationTime FrequencyData-Driven Methodshttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2Empirical mode decomposition (EMD) is an adaptive (data-driven) method to decompose non-linear and non-stationary signals into AM-FM components. Despite its well-known usefulness, one of the major EMD drawbacks is its lack of mathematical foundation, being defined as an algorithm output. In this paper we present an alternative formulation for the EMD method, based on unconstrained optimization. Unlike previous optimization-based efforts, our approach is simple, with an analytic solution, and its algorithm can be easily implemented. By making no explicit use of envelopes to find the local mean, possible inherent problems of the original EMD formulation (such as the under- and overshoot) are avoided. Classical EMD experiments with artificial signals overlapped in both time and frequency are revisited, and comparisons with other optimization-based approaches to EMD are made, showing advantages for our proposal both in recovering known components and computational times. A voice signal is decomposed by our method evidencing some advantages in comparison with traditional EMD and noise-assisted versions. The new method here introduced catches most flavors of the original EMD but with a more solid mathematical framework, which could lead to explore analytical properties of this technique.Fil: Colominas, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; ArgentinaFil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Entre Ríos. Universidad Nacional de Entre Ríos. Centro de Investigaciones y Transferencia de Entre Ríos; ArgentinaFil: Torres, Maria Eugenia. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAcademic Press Inc Elsevier Science2015-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/41591Colominas, Marcelo Alejandro; Schlotthauer, Gaston; Torres, Maria Eugenia; An unconstrained optimization approach to empirical mode decomposition; Academic Press Inc Elsevier Science; Digital Signal Processing; 40; 5-2015; 164-1751051-2004CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dsp.2015.02.013info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1051200415000706info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:13:05Zoai:ri.conicet.gov.ar:11336/41591instacron: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:34982025-09-10 13:13:05.959CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An unconstrained optimization approach to empirical mode decomposition
title An unconstrained optimization approach to empirical mode decomposition
spellingShingle An unconstrained optimization approach to empirical mode decomposition
Colominas, Marcelo Alejandro
Empirical Mode Decomposition (Emd)
Convex Optimization
Time Frequency
Data-Driven Methods
title_short An unconstrained optimization approach to empirical mode decomposition
title_full An unconstrained optimization approach to empirical mode decomposition
title_fullStr An unconstrained optimization approach to empirical mode decomposition
title_full_unstemmed An unconstrained optimization approach to empirical mode decomposition
title_sort An unconstrained optimization approach to empirical mode decomposition
dc.creator.none.fl_str_mv Colominas, Marcelo Alejandro
Schlotthauer, Gaston
Torres, Maria Eugenia
author Colominas, Marcelo Alejandro
author_facet Colominas, Marcelo Alejandro
Schlotthauer, Gaston
Torres, Maria Eugenia
author_role author
author2 Schlotthauer, Gaston
Torres, Maria Eugenia
author2_role author
author
dc.subject.none.fl_str_mv Empirical Mode Decomposition (Emd)
Convex Optimization
Time Frequency
Data-Driven Methods
topic Empirical Mode Decomposition (Emd)
Convex Optimization
Time Frequency
Data-Driven Methods
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv Empirical mode decomposition (EMD) is an adaptive (data-driven) method to decompose non-linear and non-stationary signals into AM-FM components. Despite its well-known usefulness, one of the major EMD drawbacks is its lack of mathematical foundation, being defined as an algorithm output. In this paper we present an alternative formulation for the EMD method, based on unconstrained optimization. Unlike previous optimization-based efforts, our approach is simple, with an analytic solution, and its algorithm can be easily implemented. By making no explicit use of envelopes to find the local mean, possible inherent problems of the original EMD formulation (such as the under- and overshoot) are avoided. Classical EMD experiments with artificial signals overlapped in both time and frequency are revisited, and comparisons with other optimization-based approaches to EMD are made, showing advantages for our proposal both in recovering known components and computational times. A voice signal is decomposed by our method evidencing some advantages in comparison with traditional EMD and noise-assisted versions. The new method here introduced catches most flavors of the original EMD but with a more solid mathematical framework, which could lead to explore analytical properties of this technique.
Fil: Colominas, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina
Fil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Entre Ríos. Universidad Nacional de Entre Ríos. Centro de Investigaciones y Transferencia de Entre Ríos; Argentina
Fil: Torres, Maria Eugenia. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Empirical mode decomposition (EMD) is an adaptive (data-driven) method to decompose non-linear and non-stationary signals into AM-FM components. Despite its well-known usefulness, one of the major EMD drawbacks is its lack of mathematical foundation, being defined as an algorithm output. In this paper we present an alternative formulation for the EMD method, based on unconstrained optimization. Unlike previous optimization-based efforts, our approach is simple, with an analytic solution, and its algorithm can be easily implemented. By making no explicit use of envelopes to find the local mean, possible inherent problems of the original EMD formulation (such as the under- and overshoot) are avoided. Classical EMD experiments with artificial signals overlapped in both time and frequency are revisited, and comparisons with other optimization-based approaches to EMD are made, showing advantages for our proposal both in recovering known components and computational times. A voice signal is decomposed by our method evidencing some advantages in comparison with traditional EMD and noise-assisted versions. The new method here introduced catches most flavors of the original EMD but with a more solid mathematical framework, which could lead to explore analytical properties of this technique.
publishDate 2015
dc.date.none.fl_str_mv 2015-05
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/11336/41591
Colominas, Marcelo Alejandro; Schlotthauer, Gaston; Torres, Maria Eugenia; An unconstrained optimization approach to empirical mode decomposition; Academic Press Inc Elsevier Science; Digital Signal Processing; 40; 5-2015; 164-175
1051-2004
CONICET Digital
CONICET
url http://hdl.handle.net/11336/41591
identifier_str_mv Colominas, Marcelo Alejandro; Schlotthauer, Gaston; Torres, Maria Eugenia; An unconstrained optimization approach to empirical mode decomposition; Academic Press Inc Elsevier Science; Digital Signal Processing; 40; 5-2015; 164-175
1051-2004
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dsp.2015.02.013
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1051200415000706
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
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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
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score 13.004268

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