{"title":"自相似过程小波分解的高阶和低阶性质","authors":"B. Pesquet-Popescu, P. Larzabal","doi":"10.1109/HOST.1997.613567","DOIUrl":null,"url":null,"abstract":"Self-similar processes have received increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena which exhibit \"1/f\" spectra and/or long-range dependence. On the other hand the wavelet decomposition became a very useful tool in describing nonstationary self-similar processes. In this paper we first investigate the existence and the properties of higher-order statistics of self-similar processes with finite variance. Then, we consider some self-similar processes with infinite variance and study the statistical properties of their wavelet coefficients.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"11 5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Higher and lower-order properties of the wavelet decomposition of self-similar processes\",\"authors\":\"B. Pesquet-Popescu, P. Larzabal\",\"doi\":\"10.1109/HOST.1997.613567\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Self-similar processes have received increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena which exhibit \\\"1/f\\\" spectra and/or long-range dependence. On the other hand the wavelet decomposition became a very useful tool in describing nonstationary self-similar processes. In this paper we first investigate the existence and the properties of higher-order statistics of self-similar processes with finite variance. Then, we consider some self-similar processes with infinite variance and study the statistical properties of their wavelet coefficients.\",\"PeriodicalId\":305928,\"journal\":{\"name\":\"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics\",\"volume\":\"11 5 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1997-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/HOST.1997.613567\",\"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 the IEEE Signal Processing Workshop on Higher-Order Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/HOST.1997.613567","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Higher and lower-order properties of the wavelet decomposition of self-similar processes
Self-similar processes have received increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena which exhibit "1/f" spectra and/or long-range dependence. On the other hand the wavelet decomposition became a very useful tool in describing nonstationary self-similar processes. In this paper we first investigate the existence and the properties of higher-order statistics of self-similar processes with finite variance. Then, we consider some self-similar processes with infinite variance and study the statistical properties of their wavelet coefficients.
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