Unified approach to extrapolation of bandlimited signals in linear canonical transform domain

The linear canonical transform (LCT) has been shown to be a powerful tool for signal processing and optics. Several extrapolation strategies for bandlimited signals in LCT domain have been proposed. The purpose of this paper is to present an approach that unifies a number of different algorithms for the extrapolation of bandlimited signals in LCT domain. This unification is achieved through integral equation and Hilbert space theories. First, the following existing techniques are unified: (1) a continuous signal extrapolation algorithm based on series expansion in terms of generalized prolate spheroidal functions; (2) a generalized Papoulis-Gerchberg iterative algorithm; (3) a two-step extrapolation algorithm for continuous signal from finite samples; and (4) an iterative extrapolation algorithm based on error energy reduction procedure for continuous signal from finite samples. Then, two extrapolation algorithms for discrete bandlimited signals in LCT domain are proposed, which also belongs to the unified framework.