L. R. Soares, Hélio M. de Oliveira, R. Cintra, R. Souza
{"title":"傅立叶特征函数,不确定Gabor原理和等分辨小波","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":"{\"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}","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}
Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets
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.