A closed equation in time domain for band-limited extensions of one-sided sequences

TL;DR

This paper introduces a deterministic method for optimally extending one-sided sequences using a closed linear equation in the time domain, ensuring robustness against errors through Tikhonov regularization.

Contribution

It presents a novel deterministic approach to extend semi-infinite sequences by band-limited sequences via a closed-form time domain equation, with robustness analysis.

Findings

Method effectively extends sequences with minimal error

Solution is robust to input errors and data truncation

Applicable to general types of one-sided sequences

Abstract

The paper suggests a method of optimal extension of one-sided semi-infinite sequences of a general type by traces of band-limited sequences in deterministic setting, i.e. without probabilistic assumptions. The method requires to solve a closed linear equation in the time domain connecting the past observations of the underlying process with the future values of the band-limited process. Robustness of the solution with respect to the input errors and data truncation is established in the framework of Tikhonov regularization.