{"title":"On criteria for periodic wavelet frame","authors":"Anastassia Gorsanova, Elena Lebedeva","doi":"arxiv-2409.01165","DOIUrl":null,"url":null,"abstract":"We provide constructive necessary and sufficient conditions for a family of\nperiodic wavelets to be a Parseval wavelet frame. The criterion generalizes\nunitary and oblique extension principles. It may be very useful for\napplications to signal processing because it allows to design any wavelet frame\nexplicitly starting with refinable functions. The practically important case of\none wavelet generator and refinable functions being trigonometric polynomials\nis discussed in details. As an application we study approximation properties of\nframes and give conditions for a coincidence of approximation orders provided\nby periodic multiresolution analysis and by a wavelet frame in terms of our\ncriterion.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"71 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.01165","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We provide constructive necessary and sufficient conditions for a family of
periodic wavelets to be a Parseval wavelet frame. The criterion generalizes
unitary and oblique extension principles. It may be very useful for
applications to signal processing because it allows to design any wavelet frame
explicitly starting with refinable functions. The practically important case of
one wavelet generator and refinable functions being trigonometric polynomials
is discussed in details. As an application we study approximation properties of
frames and give conditions for a coincidence of approximation orders provided
by periodic multiresolution analysis and by a wavelet frame in terms of our
criterion.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
