Convolution and correlation theorems for Wigner-Ville distribution associated with the quaternion offset linear canonical transform Convolution and correlation theorems for WVD associated with the QOLCT

The quaternion offset linear canonical transform (QOLCT) has gained much popularity in recent years because of its applications in many areas, including image and signal processing. At the same time, the applications of Wigner-Ville distribution (WVD) in signal analysis and image processing cannot be excluded. In this paper, we investigate the Wigner-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 reconstruction formula, orthogonality relation, are derived. Secondly, a novel canonical convolution operator and a related correlation operator for WVD-QOLCT are proposed. Based on the proposed operators, the corresponding generalized convolution and correlation theorems are studied. Moreover on the application part, detection of the linear frequency modulated signals is established in detail by constructing an example.