Wigner-Ville distribution associated with the quaternion linear canonical transform and their generalized uncertainty principles

Q2 Mathematics

Annali dell''Universita di Ferrara Pub Date : 2025-07-23 DOI:10.1007/s11565-025-00604-1

M. Younus Bhat, Shahbaz Rafiq, Aamir H. Dar

引用次数: 0

Abstract

Wigner-Ville distribution (WVD) in the frame work of quaternion linear canonical transform (QLCT) (WVD-QLCT) is the generalized version of WVD in the quaternion algebra. Recently, some properties and applications in detection of linear frequency modulated (LFM) signals have been studied for the WVD-QLCT. In this paper, we first establish a relationship between WVD-QLCT and QFT and then we derive different uncertainty principles (UPs) which includes the Heisenberg’s UP, logarithmic UP, Hardy’s UP, Donoho Stark’s UP and Beurling’s UP associated with the WVD-QLCT.

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与四元数线性正则变换相关的Wigner-Ville分布及其广义测不准原理

四元数线性正则变换（QLCT）框架中的Wigner-Ville分布（WVD-QLCT）是四元数代数中WVD的推广版本。近年来，人们对WVD-QLCT的一些特性及其在线性调频信号检测中的应用进行了研究。本文首先建立了WVD-QLCT与QFT之间的关系，然后推导出与WVD-QLCT相关的各种不确定性原理（UPs），包括Heisenberg UP、对数UP、Hardy UP、Donoho Stark UP和Beurling UP。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annali dell''Universita di Ferrara Mathematics-Mathematics (all)

CiteScore

1.70

自引率

0.00%

发文量

期刊介绍： Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.