The Wigner-Ville distribution associated with the quaternion offset linear canonical transform (Q2288347)

The Wigner-Ville distribution (WVD) and the quaternion offset linear canonical Fourier transform (QOLCT) are useful tools in signal analysis and image processing. The WVD is widely used for the analysis of the non-stationary signals. In the paper the authors introduce an extension of the WVD to the quaternion algebra by means of the QOLCT. The WVD-QOLC transform combines properties and flexibility of both WVD and QOLCT. The authors show how the WVD-QOLC relates to the general two-sided quaternion Fourier transform (QFT) and to the QOLCT. Using the relation between the WVD-QOLCT and the QOLCT, they obtain the inversion and Plancherel formulas for the WVD-QOLCT. Applying their earlier results related to the QFT and QOLCT, the authors establish Heisenberg's uncertainty principle and the Poisson summation formula associated with WVD-QOLCT. Finally, they formulate and prove an analogue of Lieb's theorem for the WVD-QOLCT. For this purpose they use Lieb's theorem for the quaternionic linear canonical transform.