The Extrapolation Theorem for Discrete Signals in the Offset Linear Canonical Transform Domain

The extrapolation theorem is an essential and important theory in signal analysis. Since the offset linear canonical transform (OLCT) has proven to be an effective method in signal processing and optics, extrapolation theorems for continuous band-limited signals associated with the OLCT have been well studied. However, the extrapolation theorem for discrete signals in the OLCT domain remains unknown. In this short paper, by using the discrete generalized prolate spheroidal sequences (DGPSSs), the extrapolation theorem for discrete signals is presented. First, the definition of DGPSSs in the OLCT domain is proposed. Subsequently, the extrapolation theorem for OLCT discrete band-limited signals is obtained using the DGPSSs. In addition, a simplified computation of the extrapolation theorem for discrete band-limited signals in the OLCT domain is also obtained. Finally, simulation results are presented to show the utility and efficacy of the derived theorems.