Extrapolation of Bandlimited Signals in Linear Canonical Transform Domain

The linear canonical transform (LCT) has been shown to be a powerful analyzing tool in signal processing. Many results of this transform are already known, including bandlimited extrapolation. The existing algorithm for solving the problem of LCT bandlimited extrapolation is based on signal expansion into a series of generalized prolate spheroidal wave functions (GPSWFs). However, the requirement to compute and store the GPSWFs and the errors due to the series truncation render this algorithm ill-suitable for a practical implementation. In this correspondence, we first propose a new formulation of the Gerchberg-Papoulis (GP) algorithm for LCT bandlimited extrapolation. Then, we present a fast convergence algorithm for the new formulation. The classical GP algorithm related to Fourier bandlimited signals is noted as a special case. Moreover, the comparison between the proposed algorithm and the one based on GPSWFs expansion is provided, and the validity of the theoretical derivations is demonstrated via simulations. Several potential applications of the achieved theory are also presented.