Abstract

In this article, we consider the extension of Shannon sampling series reconstruction theorem for nonhomogeneous random fields using local averages sampling, which helps improve certain earlier results. The upper bound of mean square truncation sampling approximation error is more precise, and we establish one approximation result in the almost sure sense.

中文翻译：

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从局部平均逼近非齐次随机场

摘要

在本文中，我们考虑使用局部平均采样对非齐次随机场的香农采样级数重构定理的扩展，这有助于改进某些早期结果。均方截断抽样近似误差的上界更精确，我们几乎确定地建立了一个近似结果。