Uniqueness theorem for analytic functions and its application in denoising problem

TL;DR

This paper presents a new uniqueness theorem for bounded analytic functions and demonstrates its application in the denoising problem, enabling the separation of signals from noise in systems modeled by analytic transfer functions.

Contribution

It introduces a novel uniqueness theorem for bounded analytic functions and applies it to improve noise removal in signal processing tasks.

Findings

New uniqueness theorem for bounded analytic functions

Application of theorem to signal denoising

Enhanced noise separation in system identification

Abstract

In various applications the problem of separation of the original signal and the noise arises. For example, in the identification problem for discrete linear and causal systems, the original signal consists of the values of transfer function at some points in the unit disk. In this paper we discuss the problem of choosing the points in the unite disk, for which it is possible to remove the additive noise with probability one. Since the transfer function is analytic in the unite disk, so this problem is related to the uniqueness theorems for analytic functions. Here we give a new uniqueness result for bounded analytic functions and show its applications in the denoising problem.