Framelet Sets and Associated Scaling Sets

In time–frequency analysis, an increasing interest is to develop various tools to split a signal into a set of non-overlapping frequency regions without the influence of their adjacent regions. Although the framelet is an ideal tool for time–frequency analysis, most of the framelets only give an ove...

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Autor principal:	Zhihua Zhang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	framelets set frame multiresolution analysis scaling sets Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b276db2a68b64d838e074d8f797c5731
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:b276db2a68b64d838e074d8f797c5731
record_format	dspace
spelling	oai:doaj.org-article:b276db2a68b64d838e074d8f797c57312021-11-11T18:21:16ZFramelet Sets and Associated Scaling Sets10.3390/math92128242227-7390https://doaj.org/article/b276db2a68b64d838e074d8f797c57312021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2824https://doaj.org/toc/2227-7390In time–frequency analysis, an increasing interest is to develop various tools to split a signal into a set of non-overlapping frequency regions without the influence of their adjacent regions. Although the framelet is an ideal tool for time–frequency analysis, most of the framelets only give an overlapping partition of the frequency domain. In order to obtain a non-overlapping partition of the frequency domain, framelet sets and associated scaling sets are introduced. In this study, we will investigate the relation between framelet (or scaling) sets and the frequency domain of framelets (or frame scaling functions). We find that the frequency domain of any frame scaling function always contains a scaling set and the frequency domain of any FMRA framelet always contains a framelet set. Moreover, we give a simple approach to construct various framelet/scaling sets from band-limited framelets and frame scaling functions.Zhihua ZhangMDPI AGarticleframelets setframe multiresolution analysisscaling setsMathematicsQA1-939ENMathematics, Vol 9, Iss 2824, p 2824 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	framelets set frame multiresolution analysis scaling sets Mathematics QA1-939
spellingShingle	framelets set frame multiresolution analysis scaling sets Mathematics QA1-939 Zhihua Zhang Framelet Sets and Associated Scaling Sets
description	In time–frequency analysis, an increasing interest is to develop various tools to split a signal into a set of non-overlapping frequency regions without the influence of their adjacent regions. Although the framelet is an ideal tool for time–frequency analysis, most of the framelets only give an overlapping partition of the frequency domain. In order to obtain a non-overlapping partition of the frequency domain, framelet sets and associated scaling sets are introduced. In this study, we will investigate the relation between framelet (or scaling) sets and the frequency domain of framelets (or frame scaling functions). We find that the frequency domain of any frame scaling function always contains a scaling set and the frequency domain of any FMRA framelet always contains a framelet set. Moreover, we give a simple approach to construct various framelet/scaling sets from band-limited framelets and frame scaling functions.
format	article
author	Zhihua Zhang
author_facet	Zhihua Zhang
author_sort	Zhihua Zhang
title	Framelet Sets and Associated Scaling Sets
title_short	Framelet Sets and Associated Scaling Sets
title_full	Framelet Sets and Associated Scaling Sets
title_fullStr	Framelet Sets and Associated Scaling Sets
title_full_unstemmed	Framelet Sets and Associated Scaling Sets
title_sort	framelet sets and associated scaling sets
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b276db2a68b64d838e074d8f797c5731
work_keys_str_mv	AT zhihuazhang frameletsetsandassociatedscalingsets
_version_	1718431906051129344

Framelet Sets and Associated Scaling Sets

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