{"title":"Two-dimensional biorthonormal wavelet on ZN1 × ZN2","authors":"Zhi Shi, Hai-Yan Xing, B. Peng","doi":"10.1109/ICWAPR.2009.5207487","DOIUrl":null,"url":null,"abstract":"In this paper, Fourier analysis are first presented in the two-dimensional context. Then existing work on the representation of wavelets on Z<inf>N</inf> is extented to two dimensions. A necessary and sufficient condition on the existence of biorthonormal wavelets on Z<inf>N1</inf> × Z<inf>N2</inf> is derived. A method for constructing biorthonormal wavelest on Z<inf>N1</inf> × Z<inf>N2</inf> is presented and their properties is investigated by mean of time-frequency analysis method, matrix theory and operator theory.","PeriodicalId":424264,"journal":{"name":"2009 International Conference on Wavelet Analysis and Pattern Recognition","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Conference on Wavelet Analysis and Pattern Recognition","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICWAPR.2009.5207487","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, Fourier analysis are first presented in the two-dimensional context. Then existing work on the representation of wavelets on ZN is extented to two dimensions. A necessary and sufficient condition on the existence of biorthonormal wavelets on ZN1 × ZN2 is derived. A method for constructing biorthonormal wavelest on ZN1 × ZN2 is presented and their properties is investigated by mean of time-frequency analysis method, matrix theory and operator theory.
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