Generalized uncertainty principles for offset quaternion linear canonical transform

In this work, we begin by providing a new proof of the uncertainty principle related to the quaternion linear canonical transform. We then generalize the uncertainty principles for the quaternion linear canonical transform in the literature. After defining the offset quaternion linear canonical transform and making a direct connection between the quaternion linear canonical transform and the offset quaternion linear canonical transform, we finally transfer the uncertainty principles for the quaternion linear canonical transform to the offset quaternion linear canonical transform.