{"title":"基于奈奎斯特准则的一组小波和一种新的正交多分辨率分析","authors":"Hélio M. de Oliveira, L. R. Soares, T. Falk","doi":"10.14209/jcis.2003.8","DOIUrl":null,"url":null,"abstract":"A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic Interference (ISI) elimination. An orthogonal Multiresolution Analysis (MRA) is presented, showing that the roll-off parameter should be kept below 1/3. The pass-band behaviour of the Wavelet Fourier spectrum is examined. The left and right roll-off regions are asymmetric; nevertheless the Q-constant analysis philosophy is maintained. Finally, a generalisation of the (square root) raised cosine wavelets is proposed.","PeriodicalId":310988,"journal":{"name":"Anais do 2002 International Telecommunications Symposium","volume":"106 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2003-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"A Family of Wavelets and a New Orthogonal Multiresolution Analysis Based on the Nyquist Criterion\",\"authors\":\"Hélio M. de Oliveira, L. R. Soares, T. Falk\",\"doi\":\"10.14209/jcis.2003.8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic Interference (ISI) elimination. An orthogonal Multiresolution Analysis (MRA) is presented, showing that the roll-off parameter should be kept below 1/3. The pass-band behaviour of the Wavelet Fourier spectrum is examined. The left and right roll-off regions are asymmetric; nevertheless the Q-constant analysis philosophy is maintained. Finally, a generalisation of the (square root) raised cosine wavelets is proposed.\",\"PeriodicalId\":310988,\"journal\":{\"name\":\"Anais do 2002 International Telecommunications Symposium\",\"volume\":\"106 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Anais do 2002 International Telecommunications Symposium\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14209/jcis.2003.8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Anais do 2002 International Telecommunications Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14209/jcis.2003.8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Family of Wavelets and a New Orthogonal Multiresolution Analysis Based on the Nyquist Criterion
A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic Interference (ISI) elimination. An orthogonal Multiresolution Analysis (MRA) is presented, showing that the roll-off parameter should be kept below 1/3. The pass-band behaviour of the Wavelet Fourier spectrum is examined. The left and right roll-off regions are asymmetric; nevertheless the Q-constant analysis philosophy is maintained. Finally, a generalisation of the (square root) raised cosine wavelets is proposed.
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