Higher order derivatives sampling of random signals related to the fractional Fourier transform

Multirate or multichannel sampling related theory and methods are some of the hottest research topics in modern signal processing community. Among them, the sampling associated with the signal and its derivatives is often encountered in various real applications. In this paper, we investigate the sampling theory related to the higher order derivatives of random signals with the fractional Fourier transform. We first obtain the uniform sampling theorem associated with the higher order derivatives of random signals, and then we generalize this results associated with the periodic nonuniform sampling model for random signals. The corresponding sampling rate will be reduced by a factor of n so that the workload will be greatly reduced. Finally, the simulations are performed to verify the proposed theorem.