{"title":"快速收敛的样本加权函数","authors":"F. Haber","doi":"10.1109/TCOM.1964.1088885","DOIUrl":null,"url":null,"abstract":"In this communication, a family of sampling formulas are developed which have better convergence properties than the standard formula based on amplitude samples taken at the Nyquist rate. Sampling is done at higher than the minimum rate and a sampling function, whose Fourier transform has cosine tapered skirts, is used. Suitable choice of the taper results in a formula with no \"crosstalk\" at the sampling instants. Interpolation between samples generally requires fewer samples than required by the standard formula. Tables and curves for several cases are provided.","PeriodicalId":179779,"journal":{"name":"IEEE Transactions on Communications Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1964-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Rapidly converging sample weighting functions\",\"authors\":\"F. Haber\",\"doi\":\"10.1109/TCOM.1964.1088885\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this communication, a family of sampling formulas are developed which have better convergence properties than the standard formula based on amplitude samples taken at the Nyquist rate. Sampling is done at higher than the minimum rate and a sampling function, whose Fourier transform has cosine tapered skirts, is used. Suitable choice of the taper results in a formula with no \\\"crosstalk\\\" at the sampling instants. Interpolation between samples generally requires fewer samples than required by the standard formula. Tables and curves for several cases are provided.\",\"PeriodicalId\":179779,\"journal\":{\"name\":\"IEEE Transactions on Communications Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1964-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Communications Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/TCOM.1964.1088885\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Communications Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TCOM.1964.1088885","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this communication, a family of sampling formulas are developed which have better convergence properties than the standard formula based on amplitude samples taken at the Nyquist rate. Sampling is done at higher than the minimum rate and a sampling function, whose Fourier transform has cosine tapered skirts, is used. Suitable choice of the taper results in a formula with no "crosstalk" at the sampling instants. Interpolation between samples generally requires fewer samples than required by the standard formula. Tables and curves for several cases are provided.
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