Noniterative and fast iterative methods for interpolation and extrapolation

In this correspondence we study the band-limited interpolation and extrapolation problems for finite-dimensional signals. We show that these problems can be easily reduced to the solution of a set of linear equations with a real symmetric positive-definite matrix S with spectral radius ρ(S)<1. Thus, the equations can be solved directly or using successive approximation methods. A number of other well known methods which may substantially increase the convergence rate may also be readily applied and are briefly discussed. We state conditions for their convergence, and illustrate their performance through an example