The Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform

被引：14

作者：

El Kassimi, M. ^{[1
]}

El Haoui, Y. ^{[1
]}

Fahlaoui, S. ^{[1
]}

机构：

[1] Univ Moulay Ismail, Fac Sci, Dept Math & Comp Sci, Equipe Anal Harmon & Probabil, BP 11201 Zitoune, Meknes, Morocco

来源：

ANALYSIS MATHEMATICA | 2019年 / 45卷 / 04期

关键词：

Wigner-Ville distribution; offset linear canonical transform; linear canonical transform; quaternionic transform; Heisenberg uncertainty; Poisson summation formula; Lieb's inequality; FOURIER-TRANSFORM;

D O I：

10.1007/s10476-019-0007-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Wigner-Ville distribution (WVD) and the quaternion offset linear canonical transform (QOLCT) are useful tools in signal analysis and image processing. The purpose of this paper is to define the Wigner-Ville distribution associated with the quaternionic offset linear canonical transform (WVD-QOLCT). Actually, this transform combines both the results and flexibility of the two transforms WVD and QOLCT. We derive some important properties of this transform such as inversion and Plancherel formulas, we establish a version of the Heisenberg inequality, Lieb's theorem and we give the Poisson summation formula for the WVD-QOLCT.

引用

页码：787 / 802

页数：16

共 26 条

[1] OPTICAL OPERATIONS ON WAVE-FUNCTIONS AS THE ABELIAN SUBGROUPS OF THE SPECIAL AFFINE FOURIER TRANSFORMATION [J].