Relationships among various definitions of two-dimensional quaternion linear canonical transforms

摘要

ublishercopyright>? 2019 International Association of Engineers.? 2019 International Association of Engineers. The quaternion linear canonical transforms (QLCT) is a nontrivial generalization of the linear canonical transform (LCT) using quaternion algebra. Due to the noncommutative property of quaternion multiplication there are different definitions for the QLCT. We establish the relationships among different types of the QLCTs.The quaternion linear canonical transforms (QLCT) is a nontrivial generalization of the linear canonical transform (LCT) using quaternion algebra. Due to the noncommutative property of quaternion multiplication there are different definitions for the QLCT. We establish the relationships among different types of the QLCTs.