Wigner-Ville distribution associated with the quaternion offset linear canonical transforms

2018/11/30 by Mohammed El Kassimi, Kassimi, Mohammed El, Youssef El Haoui +3 · 1 citation
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1901.01097

openalex publication_date 2018/11/30 · openalex created_date 2019/01/11 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Lens-System Diffraction Integral Written in Terms of Matrix Optics*

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