Concerning the Recovery of a Bandlimited Signal or Its Spectrum from a Finite Segment

The relationship between the iterative techniques of Sandberg and Papoulis is clarified. The conditions of Sandberg's theorem are not satisfied in general when the problem is that of extrapolating a bandlimited signal outside of a known segment (a problem that is "illposed"). For an interesting special case, the iteration may be applied and the signal recovered exactly.