二元Poisson求和公式及Shannon型样本定理  

On double-variable Poisson summation formula and Shannon type sampling theorem

作　　者：曹军[1] 陈湧涛 

机构地区：[1]玉溪师范学院数学系,云南玉溪653100 [2]曲靖师范学院数学系,云南曲靖655000

出　　处：《云南师范大学学报（自然科学版）》2002年第5期5-11,共7页Journal of Yunnan Normal University:Natural Sciences Edition

摘　　要：经典的 Shannon样本定理是关于用可数个样本点的信息对有限带 (Band-limited)信号函数进行恢复。文章利用二元 Poisson求和公式证明了未必带有限的二元函数的 Shannon型样本定理。文中所有结论不难推广到 n(>2 )The classical Shannon sampling theorem is concerned with the representation of band-limited signal functions by a sum built up from a countable number of samples over the real axis R. In the present article, the double-variable Poisson summation formula is used to deduce the double-variable Shannon type sampling theorem for not necessarily band-limited functions. So it is not difficult to generalize all the results in the present article into the case of multi-variable functions.

关 键 词：二元Poisson求和公式 Shannon型样本定理 FOURIER变换 有限带函数 二元样本定理 二元函数 

分 类 号：O174.1[理学—数学]