Uncertainty principles associated with quaternionic linear canonical transforms. (9th February 2016)

• Record Type: Journal Article
• Authors: Kou, Kit Ian; Ou, Jianyu; Morais, Joao
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 10(2016:Jul. 15)
• Page Start: 2722
• Page End: 2736
• Publication Date: 2016-02-09
• Subjects: quaternion analysis -- quaternionic Fourier transform -- quaternionic linear canonical transform -- uncertainly principle -- hypercomplex functions -- quantum mechanics -- Gaussian quaternionic signal; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3724
• Languages: English
• ISSNs: 0170-4214

Abstract

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.