Abstract
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.
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20 October 2021
An Erratum to this paper has been published: https://doi.org/10.1007/s10476-021-0107-5
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El Kassimi, M., El Haoui, Y. & Fahlaoui, S. The Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform. Anal Math 45, 787–802 (2019). https://doi.org/10.1007/s10476-019-0007-0
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DOI: https://doi.org/10.1007/s10476-019-0007-0
Key words and phrases
- Wigner-Ville distribution
- offset linear canonical transform
- linear canonical transform
- quaternionic transform
- Heisenberg uncertainty
- Poisson summation formula
- Lieb’s inequality