On recovery of signals with single point spectrum degeneracy

TL;DR

This paper investigates the recovery of discrete signals with missing data, demonstrating recoverability when the Z-transform vanishes at a single point, and provides explicit transfer functions along with robustness analysis.

Contribution

It introduces conditions for recovering signals with a single point spectrum degeneracy and explicitly constructs the transfer functions for the recovery kernels.

Findings

Recovery is possible for signals with Z-transform vanishing at a single point.

Explicit transfer functions for recovery kernels are derived.

Robustness of recovery against data truncation and noise is established.

Abstract

The paper study recovery problem for discrete time signals with a finite number of missing values. The paper establishes recoverability of these missing values for signals with Z-transform vanishing with a certain rate at a single point. The transfer functions for the corresponding recovering kernels are presented explicitly. Some robustness of the recovery with respect to data truncation or noise contamination is established.