Discrete and Continuous Band-Limited Signal Extrapolation

This paper has two main purposes. First, some new algorithms for the extrapolation of multidimensional band-limited sequences are presented. These algorithms extend those given in [1] in two ways: 1) We do not impose any restrictions on either the shape of the region containing the set of samples of the two-dimensional signal to be extrapolated or on the shape of its passband zone. 2) We obtain a class of sequences which are band-limited extrapolations of the given data (including the minimum norm solution of [1] as a special case). The second objective of our paper is to relate the discrete extrapolation problem to the continuous signal extrapolation problem [2]. Specifically, we prove that the solution obtained by using our approach for the discrete extrapolation problem tends to the solution of the continuous problem when the sampling rate used in the known part of the continuous signal to be extrapolated approaches infinity.