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.

中文翻译：

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与四元数偏移线性正则变换相关的 Wigner-Ville 分布

Wigner-Ville 分布 (WVD) 和四元数偏移线性规范变换 (QOLCT) 是信号分析和图像处理中的有用工具。本文的目的是定义与四元数偏移线性正则变换 (WVD-QOLCT) 相关的 Wigner-Ville 分布。实际上，这种变换结合了 WVD 和 QOLCT 两种变换的结果和灵活性。我们推导出了这种变换的一些重要性质，例如反演和普朗切雷尔公式，我们建立了海森堡不等式、李布定理的一个版本，并给出了 WVD-QOLCT 的泊松求和公式。