Shannon-type sampling for multivariate non-bandlimited signals

作     者：CHEN QiuHui QIAN Tao LI YouFa 

作者机构：Cisco School of InformaticsGuangdong University of Foreign Studies Department of MathematicsFaculty of Science and TechnologyUniversity of Macao College of Mathematics and Information SciencesGuangxi University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第9期

页      面：1915-1934页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 080401[工学-精密仪器及机械] 0804[工学-仪器科学与技术] 080402[工学-测试计量技术及仪器] 

基　　金：National Natural Science Foundation of China (Grant Nos. 61072126 and 11126343) Natural Science Foundation of Guangdong Province (Grant No. S2011010004986) Guangxi Natural Science Foundation (Grant No. 2013GXNSFBA019010) University of Macao (MYRG) MYRG 116(Y1-L3)-FST13-QT Macao Science and Technology Research Fund FDCT 098/2012/A3 

主　　题：analytic function Fourier transform radial Bessel-Sinc function Shannon sampling 

摘      要：In this paper, starting from a function analytic in a neighborhood of the unit disk and based on Bessel functions, we construct a family of generalized multivariate sinc functions, which are radial and named radial Bessel-sinc (RBS) functions being time-frequency atoms with nonlinear phase. We obtain a recursive formula for the RBS functions in R d with d being odd. Based on the RBS function, a corresponding sampling theorem for a class of non-bandlimited signals is established. We investigate a class of radial functions and prove that each of these functions can be extended to become a monogenic function between two parallel planes, where the monogencity is taken to be of the Clifford analysis sense.