Journal of Applied Mathematics
Volume 2012 (2012), Article ID 740161, 14 pages
Research Article

Wigner-Ville Distribution Associated with the Linear Canonical Transform

School of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 1 January 2012; Revised 24 April 2012; Accepted 13 May 2012

Academic Editor: Carlos J. S. Alves

Copyright © 2012 Rui-Feng Bai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates the Wigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of Wigner-Ville distribution associated with the linear canonical transform is given. Then, the main properties of the newly defined Wigner-Ville transform are investigated in detail. Finally, the applications of the newly defined Wigner-Ville transform in the linear-frequency-modulated signal detection are proposed, and the simulation results are also given to verify the derived theory.