The two‐sided short‐time quaternionic offset linear canonical transform and associated convolution and correlation

Abstract

In this paper, we introduce the two‐dimensional short‐time quaternion offset linear canonical transform (ST‐QOLCT), which is a generalization of the classical short‐time offset linear canonical transform (ST‐OLCT) in quaternion algebra setting. Several useful properties of the ST‐QOLCT are obtained from the properties of the ST‐QOLCT kernel. Based on the properties of the ST‐QOLCT and the convolution and correlation operators associated with QOLCT, we derive convolution and correlation theorems for the ST‐QOLCT. Finally, some potential applications of the ST‐QOLCT are introduced.