{"title":"一类广义正交函数","authors":"L. Fortuna, M. Frasca, M. Xibilia","doi":"10.1109/ECCTD.2013.6662193","DOIUrl":null,"url":null,"abstract":"In this paper a new class of orthonormal functions which includes as particular case the Laguerre filters are introduced. These functions are defined as the product of a fixed transfer function of order n and of an all-pass filter of order n × h for any n and h. The orthogonality of these functions is proven in the general case. Moreover, the singular values of the sum of the first Nh members of this class are shown to be all equal to the orthonormalization constant.","PeriodicalId":342333,"journal":{"name":"2013 European Conference on Circuit Theory and Design (ECCTD)","volume":"227 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A class of generalized orthonormal functions\",\"authors\":\"L. Fortuna, M. Frasca, M. Xibilia\",\"doi\":\"10.1109/ECCTD.2013.6662193\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper a new class of orthonormal functions which includes as particular case the Laguerre filters are introduced. These functions are defined as the product of a fixed transfer function of order n and of an all-pass filter of order n × h for any n and h. The orthogonality of these functions is proven in the general case. Moreover, the singular values of the sum of the first Nh members of this class are shown to be all equal to the orthonormalization constant.\",\"PeriodicalId\":342333,\"journal\":{\"name\":\"2013 European Conference on Circuit Theory and Design (ECCTD)\",\"volume\":\"227 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2013 European Conference on Circuit Theory and Design (ECCTD)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ECCTD.2013.6662193\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 European Conference on Circuit Theory and Design (ECCTD)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ECCTD.2013.6662193","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper a new class of orthonormal functions which includes as particular case the Laguerre filters are introduced. These functions are defined as the product of a fixed transfer function of order n and of an all-pass filter of order n × h for any n and h. The orthogonality of these functions is proven in the general case. Moreover, the singular values of the sum of the first Nh members of this class are shown to be all equal to the orthonormalization constant.
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