Sampling formulas for non-bandlimited quaternionic signals

In this paper, sampling theorems for certain types of non-bandlimited quaternionic signals are proposed. We show that the non-bandlimited quaternionic signal can be reconstructed from its samples as well as the samples of its generalized Hilbert transforms associated with quaternion Fourier and linear canonical transform. Some simulations are provided to show how the sampling formulas can be used in applications.