L. R. Soares, Hélio M. de Oliveira, R. Cintra, R. Souza
{"title":"Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets","authors":"L. R. Soares, Hélio M. de Oliveira, R. Cintra, R. Souza","doi":"10.14209/sbrt.2003.372","DOIUrl":null,"url":null,"abstract":"Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint time-frequency analysis is introduced. It is shown that any Fourier eigenfunction achieve isoresolution. It is shown that an isoresolution wavelet can be derived from each known wavelet family by a suitable scaling.","PeriodicalId":325953,"journal":{"name":"Anais do XX Simpósio Brasileiro de Telecomunicações","volume":"63 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Anais do XX Simpósio Brasileiro de Telecomunicações","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14209/sbrt.2003.372","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 17
Abstract
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint time-frequency analysis is introduced. It is shown that any Fourier eigenfunction achieve isoresolution. It is shown that an isoresolution wavelet can be derived from each known wavelet family by a suitable scaling.
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