Nonuniform sampling theorems for random signals in the offset linear canonical transform domain

With the rapid development of the offset linear canonical transform (OLCT) in the fields of optics and signal processing, it is necessary to consider the nonuniform sampling associated with the OLCT. Nowadays, the analysis and applications of the nonuniform sampling for deterministic signals in the OLCT domain have been well published and studied. However, none of the results about the reconstruction of nonuniform sampling for random signals in the OLCT domain have been proposed until now. In this paper, the nonuniform sampling and reconstruction of random signals in the OLCT domain are investigated. Firstly, a brief introduction to the fundamental knowledge of the OLCT and some special nonuniform sampling models are given. Then, the reconstruction theorems for random signals from nonuniform samples in the OLCT domain have been derived for different nonuniform sampling models. Finally, the simulation results are given to verify the accuracy of theoretical results.