The linear canonical transform (LCT) is an important tool in the nonstationary signal processing. In this paper, we analyze the random signals in the LCT domain by a more general manner. The linear canonical chirp stationary and LCT power spectral density are first derived by the nature or the physical meaning of them. Then, a new defined Wigner-Ville distribution (WVD) associated with LCT is proposed and simulated. It can be regarded as another representation of the stationarity because it is independent of the instantaneous time.