摘要
讨论带限函数的Shannon采样定理截断误差的点态、一致和积分3种估计.对于点态情形,用Dirichlet核的计算方法算出截断误差的阶为O(1/N);对于一致情形和积分情形,当函数满足一定的衰减条件时,可分别得到收敛阶的一致及积分估计.
In this paper we discuss the truncated error estimate on Shannon sampling theorem of bandlimited functions. We mainly focus on error of pointwise typo, uniform type and integral type. In pointwise type, we use the method of calculating Dirichlet kernel and obtain the order O(1/N); in uniform and integral type, by calculating the decaying condition imposed on the function, we can get the uniform and integral estimate
出处
《中国科学院研究生院学报》
CAS
CSCD
2008年第4期460-466,共7页
Journal of the Graduate School of the Chinese Academy of Sciences
基金
国家自然科学基金(10571014
10631080)资助
关键词
截断误差
点态估计
一致估计
积分估计
truncated error
pointwise estimate
uniform estimate
integral estimate