{"title":"ZN1 × ZN2上的二维双正交小波","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":"{\"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}","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}
Two-dimensional biorthonormal wavelet on ZN1 × ZN2
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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