Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms

Abstract

The Heisenberg uncertainty principle of harmonic analysis plays an important role in modern applied mathematical applications, signal processing and physics community. The generalizations and extensions of the classical uncertainty principle to the novel transforms are becoming one of the most hottest research topics recently. In this paper, we firstly obtain the uncertainty principle for Wigner-Ville distribution and ambiguity function associate with the linear canonical transform, and then the $n$-dimensional cases are investigated in detail based on the proposed Heisenberg uncertainty principle of the $n$-dimensional linear canonical transform.