Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions

被引：3
|
作者：
Li, Youfa [1 ,2 ]
Chen, Qiuhui [3 ]
Qian, Tao [2 ]
Wang, Yi [4 ]
机构：
[1] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Peoples R China
[2] Univ Macau, Dept Math, Fac Sci & Technol, Taipa, Peoples R China
[3] Guangdong Univ Foreign Studies, Cisco Sch Informat, Guangzhou, Guangdong, Peoples R China
[4] Auburn Univ, Dept Math, Montgomery, AL 36124 USA
来源：
APPLICABLE ANALYSIS | 2014年 / 93卷 / 02期
基金：
中国国家自然科学基金;
关键词：
generalized sinc function; non-bandlimited signal; sampling theorem; truncated error; noisy error; reproducing property; Sobolev smoothness; 41; 65; POLYNOMIAL DECAY-RATE; THEOREM;
D O I：
10.1080/00036811.2013.769135
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized sinc functions. This paper studies the error of the reconstructed non-bandlimited signal when an adaptive truncation scheme is employed. Further, when there are noises present in the samples, estimation on the expectation and variance of the error pertinent to the reconstructed signal is also given. Finally discussed are the reproducing properties and the Sobolev smoothness of functions in the space of non-bandlimited signals that admits such a sampling formula.
引用
收藏
页码：305 / 315
页数：11
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