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Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle
Joint Authors
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-09-09
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
A definition of the two-dimensional quaternion linear canonical transform (QLCT) is proposed.
The transform is constructed by substituting the Fourier transform kernel with the quaternion Fourier transform (QFT) kernel in the definition of the classical linear canonical transform (LCT).
Several useful properties of the QLCT are obtained from the properties of the QLCT kernel.
Based on the convolutions and correlations of the LCT and QFT, convolution and correlation theorems associated with the QLCT are studied.
An uncertainty principle for the QLCT is established.
It is shown that the localization of a quaternion-valued function and the localization of the QLCT are inversely proportional and that only modulated and shifted two-dimensional Gaussian functions minimize the uncertainty.
American Psychological Association (APA)
Bahri, Mawardi& Ashino, Ryuichi. 2019. Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle. Journal of Mathematics،Vol. 2019, no. 2019, pp.1-13.
https://search.emarefa.net/detail/BIM-1181350
Modern Language Association (MLA)
Bahri, Mawardi& Ashino, Ryuichi. Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle. Journal of Mathematics No. 2019 (2019), pp.1-13.
https://search.emarefa.net/detail/BIM-1181350
American Medical Association (AMA)
Bahri, Mawardi& Ashino, Ryuichi. Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle. Journal of Mathematics. 2019. Vol. 2019, no. 2019, pp.1-13.
https://search.emarefa.net/detail/BIM-1181350
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1181350