arXivDaily arXiv每日学术速递 周一至周五更新
arXiv math/0307313math.NAcs.NAmath-phmath.FAmath.MP
收藏

离散设置中的Wigner测度：采样与重构算子的高频分析

Wigner measures in the discrete setting: high-frequency analysis of sampling & reconstruction operators

Fabricio Macia

阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文利用Wigner测度分析采样与重构算子对函数序列高频行为的影响，给出显式公式并刻画保留或过滤高频行为的算子。

摘要：

本文旨在理解$\mathbb{R}^{d}$中函数序列的振荡和集中效应如何被规则网格上的采样和重构算子所修改。我们的分析基于Wigner测度和缺陷测度，它们为$L^{2}(\mathbb{R}^{d})$中有界序列的高频行为提供了定量描述。我们实际上给出了显式公式，使得能够计算采样/重构序列的这些测度。因此，我们能够刻画保留或过滤特定类别序列高频行为的采样和重构算子。我们结果的证明依赖于与离散函数序列相关的Wigner测度的构造和操作。

英文摘要：

The goal of this article is that of understanding how the oscillation and concentration effects developed by a sequence of functions in $\mathbb{R}^{d} $ are modified by the action of Sampling and Reconstruction operators on regular grids. Our analysis is performed in terms of Wigner and defect measures, which provide a quantitative description of the high frequency behavior of bounded sequences in $L^{2}(mathbb{R}^{d}) $. We actually present explicit formulas that make possible to compute such measures for sampled/reconstructed sequences. As a consequence, we are able to characterize sampling and reconstruction operators that preserve or filter the high-frequency behavior of specific classes of sequences. The proofs of our results rely on the construction and manipulation of Wigner measures associated to sequences of discrete functions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑