Abstract and Applied Analysis
Volume 2013 (2013), Article ID 725952, 14 pages
http://dx.doi.org/10.1155/2013/725952
Research Article

On Uncertainty Principle for Quaternionic Linear Canonical Transform

Kit Ian Kou,1 Jian-Yu Ou,1 and Joao Morais2

1Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau
2Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Portugal

Received 9 November 2012; Revised 20 March 2013; Accepted 20 March 2013

Academic Editor: Natig M. Atakishiyev

Copyright © 2013 Kit Ian Kou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we establish an uncertainty principle for the 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 2D Gaussian signal minimizes the uncertainty.