On Uncertainty Principle for Quaternionic Linear Canonical Transform. (23rd April 2013)

• Record Type: Journal Article
• Authors: Kou, Kit Ian; Ou, Jian-Yu; Morais, Joao
• Other Names: Atakishiyev Natig M. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-04-23
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/725952
• Languages: English
• ISSNs: 1085-3375

Abstract

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.