{"title":"Time-varying filter banks and multiwavelets","authors":"Martin Vetterli, G. Strang","doi":"10.1109/DSP.1994.379836","DOIUrl":null,"url":null,"abstract":"A wavelet construction by Geronimo, Hardin and Massopust uses more than one wavelet and scaling function. Strang and Strela gave a filter bank interpretation of that result, as well as a condition for moment properties of the resulting wavelets. The present authors are concerned with the regularity of the resulting iterated filter bank scheme, that is, a matrix extension of the classic result by Daubechies (1988) on iterated filters. They show in particular: (i) the relation between time-varying filter banks and multiwavelets, (ii) the construction of multiwavelets as limits of iterated time-varying filter banks, (iii) a necessary condition for the convergence of the iterated matrix product and (iv) an exploration of examples of multiwavelets as iterations of time-varying filter banks.<<ETX>>","PeriodicalId":189083,"journal":{"name":"Proceedings of IEEE 6th Digital Signal Processing Workshop","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1994-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"41","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of IEEE 6th Digital Signal Processing Workshop","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DSP.1994.379836","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 41
Abstract
A wavelet construction by Geronimo, Hardin and Massopust uses more than one wavelet and scaling function. Strang and Strela gave a filter bank interpretation of that result, as well as a condition for moment properties of the resulting wavelets. The present authors are concerned with the regularity of the resulting iterated filter bank scheme, that is, a matrix extension of the classic result by Daubechies (1988) on iterated filters. They show in particular: (i) the relation between time-varying filter banks and multiwavelets, (ii) the construction of multiwavelets as limits of iterated time-varying filter banks, (iii) a necessary condition for the convergence of the iterated matrix product and (iv) an exploration of examples of multiwavelets as iterations of time-varying filter banks.<>
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
