Extrapolation Theorem for Bandlimited Signals Associated with the Offset Linear Canonical Transform

The offset linear canonical transform (OLCT) is a novel and effective method in signal processing and optics. Many important properties and results of the OLCT have been well studied and published. However, the extrapolation theorem of the OLCT bandlimited signals still remains unknown. In this short paper, by using the generalized prolate spheroidal wave functions (GPSWFs), the extrapolation theorem for the OLCT bandlimited signals has been provided. Firstly, the concept of the GPSWFs in the OLCT domain has been proposed. Subsequently, the dual orthogonality and completeness of the GPSWFs associated with the OLCT have been derived based on the definition. In addition, the extrapolation theorem of the OLCT bandlimited signals has been obtained by using the orthogonality and completeness properties of the GPSWFs. Finally, the simulation results are presented to show the usefulness and effectiveness of the derived theorems.