{"title":"周期移不变多分辨率分析","authors":"A. Bastys","doi":"10.1109/DSPWS.1996.555545","DOIUrl":null,"url":null,"abstract":"The Shannon multiresolution analysis and two methods of its periodization are considered. The class of all shift-invariant multiperiodic analyses with complex-valued scaling functions is described. All weakly shift-invariant periodic analogues of the Shannon scaling function are found. Among them, two shift-invariant periodic analogues of the sine function are revealed. A wavelet packet transform that generalizes the discrete Fourier transformation is found. An application of the shift-invariant periodic wavelet packet bases for time-frequency analysis of speech signals is discussed and illustrated.","PeriodicalId":131323,"journal":{"name":"1996 IEEE Digital Signal Processing Workshop Proceedings","volume":"175 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1996-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Periodic shift-invariant multiresolution analysis\",\"authors\":\"A. Bastys\",\"doi\":\"10.1109/DSPWS.1996.555545\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Shannon multiresolution analysis and two methods of its periodization are considered. The class of all shift-invariant multiperiodic analyses with complex-valued scaling functions is described. All weakly shift-invariant periodic analogues of the Shannon scaling function are found. Among them, two shift-invariant periodic analogues of the sine function are revealed. A wavelet packet transform that generalizes the discrete Fourier transformation is found. An application of the shift-invariant periodic wavelet packet bases for time-frequency analysis of speech signals is discussed and illustrated.\",\"PeriodicalId\":131323,\"journal\":{\"name\":\"1996 IEEE Digital Signal Processing Workshop Proceedings\",\"volume\":\"175 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1996-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1996 IEEE Digital Signal Processing Workshop Proceedings\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/DSPWS.1996.555545\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1996 IEEE Digital Signal Processing Workshop Proceedings","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DSPWS.1996.555545","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Shannon multiresolution analysis and two methods of its periodization are considered. The class of all shift-invariant multiperiodic analyses with complex-valued scaling functions is described. All weakly shift-invariant periodic analogues of the Shannon scaling function are found. Among them, two shift-invariant periodic analogues of the sine function are revealed. A wavelet packet transform that generalizes the discrete Fourier transformation is found. An application of the shift-invariant periodic wavelet packet bases for time-frequency analysis of speech signals is discussed and illustrated.
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