The extrapolation of bandlimited signals in the offset linear canonical transform domain

The extrapolation theorem is a fundamental and important theory in signal analysis. As the offset linear canonical transform (OLCT) has proven to be a novel and effective method in signal processing and optics, a variety of properties and theories of the OLCT have been well studied. However, there are still no papers considered the extrapolation theorem for the OLCT bandlimited signals. Therefore in this paper, the extrapolation of the bandlimited signals associated with the OLCT based on the Gerchberg-Papoulis (GP) method has been presented for the first time. First, a useful theorem for the generalized prolate spheroidal wave function (GPSWFs) has been introduced. Then, the extrapolation of bandlimited signals in the OLCT domain has been derived based on this theorem by using the GP algorithm. Moreover, a fast computation of the extrapolation theorem in the OLCT domain also has been attained. Finally, the numerical results have been carried out to show the effective and useful of the proposed results.