{"title":"延长移位帧和它们的双联","authors":"J. Hogan, J. Lakey","doi":"10.1109/SAMPTA.2015.7148862","DOIUrl":null,"url":null,"abstract":"We investigate frames for the Paley-Wiener space PW<sub>Ω</sub> of square-integrable functions bandlimited to [-Ω/2, Ω/2] generated by translates φ<sub>n</sub> (t - αℓ) of prolate spheroidal wave-functions ψ<sub>n</sub> (where α > 0 and ℓ is an integer). We estimate frame bounds and give a Fourier construction of the dual frames. An ℓ<sup>2</sup> estimate on the decay of uniform samples of prolate functions is given to show that the computation of the duals can be done efficiently.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Prolate shift frames and their duals\",\"authors\":\"J. Hogan, J. Lakey\",\"doi\":\"10.1109/SAMPTA.2015.7148862\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate frames for the Paley-Wiener space PW<sub>Ω</sub> of square-integrable functions bandlimited to [-Ω/2, Ω/2] generated by translates φ<sub>n</sub> (t - αℓ) of prolate spheroidal wave-functions ψ<sub>n</sub> (where α > 0 and ℓ is an integer). We estimate frame bounds and give a Fourier construction of the dual frames. An ℓ<sup>2</sup> estimate on the decay of uniform samples of prolate functions is given to show that the computation of the duals can be done efficiently.\",\"PeriodicalId\":311830,\"journal\":{\"name\":\"2015 International Conference on Sampling Theory and Applications (SampTA)\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-05-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 International Conference on Sampling Theory and Applications (SampTA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SAMPTA.2015.7148862\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 International Conference on Sampling Theory and Applications (SampTA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SAMPTA.2015.7148862","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We investigate frames for the Paley-Wiener space PWΩ of square-integrable functions bandlimited to [-Ω/2, Ω/2] generated by translates φn (t - αℓ) of prolate spheroidal wave-functions ψn (where α > 0 and ℓ is an integer). We estimate frame bounds and give a Fourier construction of the dual frames. An ℓ2 estimate on the decay of uniform samples of prolate functions is given to show that the computation of the duals can be done efficiently.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
