关于随机场的傅立叶谱和Walsh–Rademacher谱之间的关系

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2023-10-13 DOI:10.1016/j.acha.2023.101603

Anton Kutsenko , Sergey Danilov , Stephan Juricke , Marcel Oliver

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引用次数: 0

摘要

我们讨论了离散随机场的展开系数之间的关系，当针对不同的层次基进行分析时。我们主要关注两个这样的系统的比较：Walsh–Rademacher基和三角傅立叶基。一般来说，根据一个基础计算的光谱在另一个基础上看起来会有所不同。在本文中，我们证明了，在统计学意义上，在一个基础上计算的光谱衰减率可以转换为另一个基础。我们进一步提供了四边形网格上这种平移的显式表达式。用确定性场和随机场的数值例子说明了结果。

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On the relation between Fourier and Walsh–Rademacher spectra for random fields

We discuss relations between the expansion coefficients of a discrete random field when analyzed with respect to different hierarchical bases. Our main focus is on the comparison of two such systems: the Walsh–Rademacher basis and the trigonometric Fourier basis. In general, spectra computed with respect to one basis will look different in the other. In this paper, we prove that, in a statistical sense, the rate of spectral decay computed in one basis can be translated to the other. We further provide explicit expressions for this translation on quadrilateral meshes. The results are illustrated with numerical examples for deterministic and random fields.

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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.