平均采样定理

Average sampling theorem

采样定理是信号分析中的基本工具之一,广泛应用于数字信号处理、无线通信等很多领域.近年来,经典的Shannon采样定理被从频谱有限函数空间推广到更一般的平移不变子空间,采样方法也从逐点取值推广到平均采样和多通道采样等.本文简要回顾采样定理的发展过程,重点介绍一些最新研究进展,包括平均采样、多通道采样和随机过程采样等,以及混淆误差和截断误差等重构误差估计.

The sampling theorem is one of the fundamental and powerful tools in signal processing, which is widely used in digital signal processing, wireless communication, and many other fields. Recently, the classical Shannon sampling theorem has been extended from bandlimited functions to shift invariant subspaces, and from sampling function values to sampling local averages. In this paper, we simply review the development of the sampling theory with a focus on some recent advances in average sampling, multi-channel sampling and average sampling for stochastic processes. We also introduce some results on approximation errors.