{"title":"小波分析作为一种信息处理技术","authors":"Hélio M. de Oliveira, D. F. D. Souza","doi":"10.1109/ITS.2006.4433232","DOIUrl":null,"url":null,"abstract":"A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundations of a wavelet information theory (WIT). Both continuous and discrete time signals are considered. Finally, we showed how to compute the information provided by a multiresolution analysis by means of the inhomogeneous wavelet expansion. Highlighting ideas behind the WIT are presented.","PeriodicalId":271294,"journal":{"name":"2006 International Telecommunications Symposium","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Wavelet analysis as an information processing technique\",\"authors\":\"Hélio M. de Oliveira, D. F. D. Souza\",\"doi\":\"10.1109/ITS.2006.4433232\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundations of a wavelet information theory (WIT). Both continuous and discrete time signals are considered. Finally, we showed how to compute the information provided by a multiresolution analysis by means of the inhomogeneous wavelet expansion. Highlighting ideas behind the WIT are presented.\",\"PeriodicalId\":271294,\"journal\":{\"name\":\"2006 International Telecommunications Symposium\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 International Telecommunications Symposium\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ITS.2006.4433232\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 International Telecommunications Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITS.2006.4433232","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Wavelet analysis as an information processing technique
A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundations of a wavelet information theory (WIT). Both continuous and discrete time signals are considered. Finally, we showed how to compute the information provided by a multiresolution analysis by means of the inhomogeneous wavelet expansion. Highlighting ideas behind the WIT are presented.
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