Wigner-Ville分布在四元数偏移线性正则变换下的卷积和相关定理
Convolution and Correlation Theorems for Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform
摘要：
四元数偏移线性正则变换（QOLCT）由于其在彩色图像和信号处理等领域的广泛应用，近年来得到了广泛的应用。同时也不能排除Wigner-Ville分布在信号分析和图像处理中的应用。本文研究了与四元数偏移线性正则变换（WVD-QOLCT）相关联的Winger-Ville分布。首先给出了WVD-QOLCT的定义，然后推导了新定义的WVD-QOLCT的几个重要性质，如非线性、有界、重构公式、正交关系和Plancherel公式。其次，提出了一种新的WVD-QOLCT标准卷积算子和相关算子。此外，基于所提出的算子，我们还研究了相应的广义卷积和相关定理，并证明了QWVD和WVD-QLCT的卷积和相关定理可以看作是我们所得结果的特例。
英文摘要：
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.
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