The Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform

The Wigner-Ville distribution (WVD) and the quaternion offset linear canonical transform (QOLCT) are useful tools in signal analysis and image processing. The purpose of this paper is to define the Wigner-Ville distribution associated with the quaternionic offset linear canonical transform (WVD-QOLC...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2019-12, Vol.45 (4), p.787-802
Main Authors: El Kassimi, M., El Haoui, Y., Fahlaoui, S.
Format: Article
Language:English
Subjects:
Analysis
Image processing
Mathematics
Mathematics and Statistics
Quaternions
Signal analysis
Signal processing
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Summary:The Wigner-Ville distribution (WVD) and the quaternion offset linear canonical transform (QOLCT) are useful tools in signal analysis and image processing. The purpose of this paper is to define the Wigner-Ville distribution associated with the quaternionic offset linear canonical transform (WVD-QOLCT). Actually, this transform combines both the results and flexibility of the two transforms WVD and QOLCT. We derive some important properties of this transform such as inversion and Plancherel formulas, we establish a version of the Heisenberg inequality, Lieb’s theorem and we give the Poisson summation formula for the WVD-QOLCT.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-019-0007-0