On sampling of band-limited signals associated with the linear canonical transform

Sampling is one of the fundamental topics in the signal processing community. Theorems proposed under this topic form the bridge between the continuous-time signals and discrete-time signals. Several sampling theorems, which aid in the reconstruction of signals in the linear canonical transform (LCT) domain, have been proposed in the literature. However, two main practical issues associated with the sampling of the LCT still remain unresolved. The first one relates to the reconstruction of the original signal from nonuniform samples and the other issue relates to the fact that only a finite number of samples are available practically. Focusing on these issues, this paper seeks to address the above from the LCT point of view. First, we extend several previously developed theorems for signals band-limited in the Fourier domain to signals band-limited in the LCT domain, followed by the derivation of the reconstruction formulas for finite uniform or recurrent nonuniform sampling points associated with the LCT. Simulation results and the potential applications of the theorem are also proposed.