广义多元三角多项式空间中的加权随机采样与重构

IF 2 2区数学 Q1 MATHEMATICS

Analysis and Applications Pub Date : 2021-12-31 DOI:10.1142/s0219530521500330

Wei Li, Jun Xian

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引用次数: 2

摘要

三角多项式空间的采样和重构集在信号处理中起着重要的作用。然而，在许多应用中，三角多项式空间中的频率并不都是整数。研究了一般多元三角多项式空间中函数的加权随机抽样和重构问题。抽样集是随机选择在一个有界立方体上的一个概率分布。我们得到了在一般多元三角多项式空间中，当采样量足够大时，抽样不等式在绝大概率下成立，且显式重构公式对所有函数都成功。

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Weighted random sampling and reconstruction in general multivariate trigonometric polynomial spaces

The set of sampling and reconstruction in trigonometric polynomial spaces will play an important role in signal processing. However, in many applications, the frequencies in trigonometric polynomial spaces are not all integers. In this paper, we consider the problem of weighted random sampling and reconstruction of functions in general multivariate trigonometric polynomial spaces. The sampling set is randomly selected on a bounded cube with a probability distribution. We obtain that with overwhelming probability, the sampling inequality holds and the explicit reconstruction formula succeeds for all functions in the general multivariate trigonometric polynomial spaces when the sampling size is sufficiently large.

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来源期刊

Analysis and Applications 数学-数学

CiteScore

3.90

自引率

4.50%

发文量

审稿时长

>12 weeks

期刊介绍： Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. Some of the topics from analysis include approximation theory, asymptotic analysis, calculus of variations, integral equations, integral transforms, ordinary and partial differential equations, delay differential equations, and perturbation methods. The primary aim of the journal is to encourage the development of new techniques and results in applied analysis.