On recoverability of discrete time signals from sparse observations

Abstract: The paper investigates recoverability of discrete time signals represented by infinite sequences from incomplte observations. It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable signals and such that signals from these classes feature robust linear recoverability of their finite traces under very mild restrictions on the location of the observed data. In particular, the case arbitrarily sparse and non-periodic subsequences of observations are not excluded.