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Uncertainty principles associated with quaternionic linear canonical transforms |
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| Authors: | Kit Ian Kou Jianyu Ou Joao Morais |
| Affiliation: | Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China |
| 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. |
| Keywords: | quaternion analysis quaternionic Fourier transform quaternionic linear canonical transform uncertainly principle hypercomplex functions quantum mechanics Gaussian quaternionic signal |