Convolution and correlation theorems for Wigner-Ville distribution associated with the offset linear canonical transform

The Wigner-Ville distribution associated with the linear canonical transform (WVD-LCT) attracts serious attention in recent literatures. For this, currently, many time-frequency distributions are derived. In this paper, generalization of the WVD-LCT the Wigner-Ville distribution in the offset linear canonical transform (WVD-OLCT) is shown. Also various properties and applications, such as detection of the linear frequency modulated (LFM) signals are established in detail. And the much important result for this transform is that convolution and correlation theorems are derived. In other words, we generalized the WVD-LCT into the WVD-OLCT.