Reconstruction of digital spectrum from periodic nonuniformly sampled signals in offset linear canonical transform domain

Author-Highlights
• Detailed spectral analysis of periodic nonuniformly sampled one-dimensional signals in the OLCT domain have been performed.
• A relationship between the discrete and continuous OLCT spectrum has been deduced.
• A method to reconstruct the digital spectrum from periodic nonuniformly sampled signals in one-dimensional case has been proposed.
• All the theories have been extended to the two-dimensional case.

Periodic nonuniform sampling is a special case of nonuniform sampling. It arises in a broad range of applications due to imperfect timebase or random events. As the offset linear canonical transform (OLCT) has been shown to be a powerful tool for optics and signal processing, it is worthwhile and interesting to explore the spectral analysis and reconstruction for periodic nonuniformly sampled signals in the OLCT domain. In this paper, we address the problem of spectral analysis and reconstruction for periodic nonuniformly sampled signals associated with the OLCT. Firstly, detailed spectral analysis of periodic nonuniformly sampled one-dimensional signals has been performed. By applying the results, a relationship between the discrete and continuous spectrum has been deduced, and a method to reconstruct the digital spectrum from periodic nonuniformly sampled signals in one-dimensional case has been proposed. Then, we extend that theories to the two-dimensional case. Finally, the simulation results are presented to show the advantage and effectiveness of the methods.