{"title":"Scale, frequency, time, and the scale transform","authors":"L. Cohen","doi":"10.1109/SSAP.1992.246836","DOIUrl":null,"url":null,"abstract":"The author develops the relationship between time, frequency, and scale, and their respective operators and representations. A scale operator is proposed and its eigenfunctions are obtained. This leads to the scale transform. The convolution and correlation theorems for scale are developed. The concepts of filtering and linear shift-invariant systems are formulated for scale.<<ETX>>","PeriodicalId":309407,"journal":{"name":"[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing","volume":"19 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SSAP.1992.246836","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
The author develops the relationship between time, frequency, and scale, and their respective operators and representations. A scale operator is proposed and its eigenfunctions are obtained. This leads to the scale transform. The convolution and correlation theorems for scale are developed. The concepts of filtering and linear shift-invariant systems are formulated for scale.<>
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