Analysis of A-stationary random signals in the linear canonical transform domain

The notion of stationarity associated with the Fourier transform plays an important roll in random signals theory. As the linear canonical transform (LCT) has been shown to be a powerful tool in signal processing, the theories and properties of random signals in the LCT domain have been extensively studied. However, there are no results published associated with the generalized concept of stationarity for random signals in the LCT domain. Hence in this paper, the detailed analysis of A-stationary random signals in the LCT domain has been presented, which shows that for random signals are non-stationary in the standard formulation whereas can be A-stationary. First, the generalized concept of A-stationarity for random signals associated with the LCT has been introduced. Based on the concept, the LCT correlation function and the LCT power spectral density for A-stationary random signals have been derived. Then, we have redefined the notion of A-stationarity in terms of the A-Wigner-Ville distribution. In addition, the sampling theorem for A-stationary random signals have been obtained. Finally, the simulations and the potential applications are carried out to verify the validity and correctness of the proposed results.