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耦合分数维维格纳-威利分布的不确定性原理

Uncertainty principles for coupled fractional Wigner-Ville distribution.

作者信息

Nur Andi Tenri Ajeng, Bahri Mawardi, Bachtiar Nasrullah, Rahim Amran

机构信息

Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia.

出版信息

R Soc Open Sci. 2024 May 1;11(5):231579. doi: 10.1098/rsos.231579. eCollection 2024 May.

DOI:10.1098/rsos.231579
PMID:38699554
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11061801/
Abstract

The coupled fractional Wigner-Ville distribution is a more general version of the fractional Wigner-Ville distribution. Main properties including boundedness, Moyal's formula and inversion formula are studied in detail for the transformation. Additionally, the relation of the coupled fractional Wigner-Ville distribution with the two-dimensional Fourier transform is studied. We also present the relationship between the coupled fractional Wigner-Ville distribution with the two-dimensional Wigner-Ville distribution. We show how the properties and relations allow us to derive several versions of the uncertainty inequalities related to the coupled fractional Wigner-Ville distribution.

摘要

耦合分数维维格纳-威利分布是分数维维格纳-威利分布的一个更一般的版本。针对该变换，详细研究了包括有界性、莫亚尔公式和反演公式在内的主要性质。此外，还研究了耦合分数维维格纳-威利分布与二维傅里叶变换的关系。我们还给出了耦合分数维维格纳-威利分布与二维维格纳-威利分布之间的关系。我们展示了这些性质和关系如何使我们能够推导出与耦合分数维维格纳-威利分布相关的几个版本的不确定性不等式。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/c821cd432607/rsos.231579.f004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/b02e66f49e46/rsos.231579.f001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/dfe2b348a045/rsos.231579.f002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/c947e4dbd86d/rsos.231579.f003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/c821cd432607/rsos.231579.f004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/b02e66f49e46/rsos.231579.f001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/dfe2b348a045/rsos.231579.f002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/c947e4dbd86d/rsos.231579.f003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9192/11061801/c821cd432607/rsos.231579.f004.jpg

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