Uncertainty principles associated with quaternionic linear canonical transforms

Abstract

In the present paper, we generalize the linear canonical transform (LCT) to quaternion‐valued signals, known as the quaternionic LCT (QLCT). Using the properties of the LCT, we establish an uncertainty principle for the two‐sided QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion‐valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternionic signal minimizes the uncertainty. Copyright © 2016 John Wiley & Sons, Ltd.