Discrete wavelets on $\mathbb{Z}_N$

Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2014, Director: F.Javier Soria de Diego

Detalles Bibliográficos
Autor: Debernardi Pinos, Alberto
Tipo de recurso: tesis de maestría
Fecha de publicación:2014
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/63187
Acceso en línea:https://hdl.handle.net/2445/63187
Access Level:acceso abierto
Palabra clave:Ondetes (Matemàtica)
Anàlisi de Fourier
Treballs de fi de màster
Wavelets (Mathematics)
Fourier analysis
Master's theses
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spelling Discrete wavelets on $\mathbb{Z}_N$Debernardi Pinos, AlbertoOndetes (Matemàtica)Anàlisi de FourierTreballs de fi de màsterWavelets (Mathematics)Fourier analysisMaster's thesesTreballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2014, Director: F.Javier Soria de DiegoThis Master’s thesis is devoted to develop the theory of discrete (finite-dimensional) wavelets. In this context, wavelets are very concrete basis of vectors with special properties that make them suitable for the purpose of data compressing or digital signal processing, among others. Thus, this will be our ultimate goal in the study of wavelets. Since we are considering finite-dimensional vectors, the whole theory is based in linear algebraic techniques. This theory can also be extended for vectors in $\mathbb{Z}$, and for functions in $\MATHBB{R}$; actually, there will be several analogies between these different settings that will be remarked throughout the work. In fact, this theory was firstly studied in $\mathbb{R}$, being [10] and [11] its predecessors. After introducing the main results in the discrete setting, we also give several examples of data compression. Surprisingly, wavelets will allow us to reduce significantly the amount of information needed to reproduce a vector (or a matrix), which is very important for data storage and transmission, since the less information we need, the less resources we have to use.Soria de Diego, F. Javier2014info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/63187Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc-by-sa (c) Alberto Debernardi Pinos, 2014http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/631872026-05-27T06:46:51Z
dc.title.none.fl_str_mv Discrete wavelets on $\mathbb{Z}_N$
title Discrete wavelets on $\mathbb{Z}_N$
spellingShingle Discrete wavelets on $\mathbb{Z}_N$
Debernardi Pinos, Alberto
Ondetes (Matemàtica)
Anàlisi de Fourier
Treballs de fi de màster
Wavelets (Mathematics)
Fourier analysis
Master's theses
title_short Discrete wavelets on $\mathbb{Z}_N$
title_full Discrete wavelets on $\mathbb{Z}_N$
title_fullStr Discrete wavelets on $\mathbb{Z}_N$
title_full_unstemmed Discrete wavelets on $\mathbb{Z}_N$
title_sort Discrete wavelets on $\mathbb{Z}_N$
dc.creator.none.fl_str_mv Debernardi Pinos, Alberto
author Debernardi Pinos, Alberto
author_facet Debernardi Pinos, Alberto
author_role author
dc.contributor.none.fl_str_mv Soria de Diego, F. Javier
dc.subject.none.fl_str_mv Ondetes (Matemàtica)
Anàlisi de Fourier
Treballs de fi de màster
Wavelets (Mathematics)
Fourier analysis
Master's theses
topic Ondetes (Matemàtica)
Anàlisi de Fourier
Treballs de fi de màster
Wavelets (Mathematics)
Fourier analysis
Master's theses
description Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2014, Director: F.Javier Soria de Diego
publishDate 2014
dc.date.none.fl_str_mv 2014
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/63187
url https://hdl.handle.net/2445/63187
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc-by-sa (c) Alberto Debernardi Pinos, 2014
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-sa (c) Alberto Debernardi Pinos, 2014
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Màster Oficial - Matemàtica Avançada
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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