Nonuniform Sampling Theorems for Bandlimited Signals in the Offset Linear Canonical Transform

Nonuniform sampling is an important kind of sampling, which arises in various real applications due to imperfect timebase or random events. As the offset linear canonical transform (OLCT) has shown to be a powerful tool for optics and signal processing, it is therefore worthwhile and interesting to explore the nonuniform sampling theorems for deterministic signals and random signals in the OLCT domain. In this paper, we address the problem of the nonuniform sampling of deterministic signals and random signals associated with the OLCT. First, some special nonuniform sampling models are briefly introduced. Then, the reconstruction theorems for deterministic signals from these nonuniform samples in the OLCT domain have been obtained. In addition, by applying the results, the nonuniform sampling theorems for random signals in the OLCT domain also have been derived. Finally, the simulation results are presented to show the advantages and effectiveness of the methods.