{"title":"时变滤波器组和多小波","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":"{\"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}","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}
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.<>
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