Wigner-Ville distribution and ambiguity function associated with the quaternion offset linear canonical transform

Abstract

Wigner-Ville transform or Wigner-Ville distribution (WVD) associated with quaternion offset linear canonical transform (QOLCT) was proposed by Bhat and Dar. This work is devoted to the development of the theory proposed by them, which is an emerging tool in the scenario of signal processing. The main contribution of this work is to introduce WVD and ambiguity function (AF) associated with the QOLCT (WVD-QOLCT/AF-QOLCT). First, the definition of the WVD-QOLCT is proposed, and then several important properties such as dilation, nonlinearity, and boundedness are derived. Second, we derived the AF for the proposed transform. A bunch of important properties, including the reconstruction formula associated with the AF, are studied.

Keywords

• quaternion algebra
• quaternion offset linear canonical transform
• wigner-ville distribution
• ambiguity function
• dilation
• 11r52
• 42c40
• 42c30
• 43a30