The quaternion offset linear canonical transform(QOLCT) has gained much popularity in recent years because of its applications in many areas, including color image and signal processing. At the same time the applications of Wigner-Ville distribution (WVD) in signal analysis and image processing can not be excluded. In this paper we investigate the Winger-Ville Distribution associated with quaternion offset linear canonical transform (WVD-QOLCT). Firstly, we propose the definition of the WVD-QOLCT, and then several important properties of newly defined WVD-QOLCT, such as nonlinearity, bounded, reconstruction formula, orthogonality relation and Plancherel formula are derived. Secondly a novel canonical convolution operator and a related correlation operator for WVD-QOLCT are proposed. Moreover, based on the proposed operators, the corresponding generalized convolution, correlation theorems are studied.We also show that the convolution and correlation theorems of the QWVD and WVD-QLCT can be looked as a special case of our achieved results.
翻译:近些年来,由于在包括彩色图像和信号处理在内的许多领域应用了新定义的WVD-QOLCT(QOLCT),KIVNion-Ville分布(WVD)在信号分析和图像处理方面的应用是不可排除的。在本文件中,我们调查了与KIVND-QOLCT(WVD-QOLCT)相关联的线性-Ville分布(VVD-QOLCT)。首先,我们提出了WVD-QOLCT(QOLCT)的定义,然后提出了新定义的WVD-QOLCT的若干重要特性,例如非线性、约束性、重建性公式、或高度性关系和Plancherel公式。第二,我们提出了WVD-QOLCT(VD-QOLCT)的新版的Cencial condiculculal Convencial convocial和相关性。我们所取得成果的一个特殊案例。