高斯缓和广义随机过程的Wigner分布

IF 3.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2025-08-13 DOI:10.1016/j.acha.2025.101799

Patrik Wahlberg

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引用次数: 0

摘要

我们定义了复值对称高斯的调和广义随机过程的Wigner分布。给出了一个定义在相空间上的时频广义随机过程。我们研究了它的协方差，我们的主要结果是一个协方差算子的Weyl符号的公式，用原始广义随机过程的协方差算子的Weyl符号表示。

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The Wigner distribution of Gaussian tempered generalized stochastic processes

We define the Wigner distribution of a tempered generalized stochastic process that is complex-valued symmetric Gaussian. This gives a time-frequency generalized stochastic process defined on the phase space. We study its covariance and our main result is a formula for the Weyl symbol of the covariance operator, expressed in terms of the Weyl symbol of the covariance operator of the original generalized stochastic process.

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.