  The Wigner-Ville distribution (WVD) and quaternion offset linear canonical
transform (QOLCT) are a useful tools in signal analysis and image processing.
The purpose of this paper is to define the Wigner-Ville distribution associated
with quaternionic offset linear canonical transform (WVD-QOLCT). Actually, this
transform combines both the results and flexibility of the two transform WVD
and QOLCT. We derive some important properties of this transform such as
inversion and Plancherel formulas, we establish a version of Heisenberg
inequality, Lieb's theorem and we give the Poisson summation formula for the
WVD-QOLCT.
