On Recovery of Discrete Time Signals with Single-Point Spectrum Degeneracy

The paper studies recoverability of missing values for sequences in a pathwise setting without probabilistic assumptions. Sufficient conditions of recoverability are obtained; it is shown that square summable sequences are recoverable if the Z -transforms vanish at a single point. The recovery is based on a new family of transfer functions defined by locations of missing values. Some robustness of the solution with respect to noise contamination and truncation is established.