{"title":"Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets","authors":"A.M. Jarrah , Nikhil Khanna","doi":"10.1016/j.ajmsc.2018.07.001","DOIUrl":null,"url":null,"abstract":"<div><p>A formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and cross-correlation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math></span>, some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given.</p></div>","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":"25 2","pages":"Pages 169-179"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ajmsc.2018.07.001","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arab Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1319516618301531","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 10
Abstract
A formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and cross-correlation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of , some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given.
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