Sampling theorems for bandlimited random signals in the offset linear canonical transform domain

Sampling theorems for deterministic signals in the offset linear canonical transform (OLCT) domain have been widely proposed in the literature. In this paper, we consider the sampling and reconstruction schemes for random signals in the OLCT domain. We first define the power spectral density and correlation function for random signals in the OLCT domain. By utilizing the definitions, the power spectral density relations for the OLCT filter are derived. Subsequently, the multichannel sampling theorem for bandlimited random signals in the OLCT domain is derived. In addition, some sampling theorems for bandlimited random signals associated with the OLCT are also presented by designing different OLCT filters. Finally, the simulation results are presented to show the advantage and effectiveness of the theorems.