On recovering missing values for sequences in a pathwise setting

TL;DR

This paper introduces a frequency-based criterion for error-free recovery of missing sequence values in a deterministic, pathwise setting, providing explicit algorithms and robustness analysis without relying on probabilistic models.

Contribution

It establishes a new frequency criterion for error-free recovery of missing data in sequences, including non-summable cases, with explicit transfer functions and noise robustness.

Findings

Error-free recoverability for square-summable sequences with Z-transform vanishing at isolated points.

Explicit transfer functions for the recovery algorithms are provided.

The recovery method shows robustness to noise contamination.

Abstract

The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e. discrete time processes, in a pathwise setting without probabilistic assumptions. The paper establishes error-free recoverability for classes of square-summable sequences with Z-transform vanishing at isolated points with a mild rate; the case of non-summable sequences is not excluded. The transfer functions for recovering algorithm are presented explicitly. Some robustness with respect to noise contamination is established for the suggested recovering algorithm.