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Uncertainty principles associated with quaternionic linear canonical transforms
Author(s) -
Kou Kit Ian,
Ou Jianyu,
Morais Joao
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3724
Subject(s) - quaternion , mathematics , uncertainty principle , gaussian , product (mathematics) , signal (programming language) , algebra over a field , pure mathematics , computational chemistry , geometry , computer science , quantum mechanics , chemistry , physics , quantum , programming language
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.