Mathematical properties of a semi-classical signal analysis method: noisy signal case

TL;DR

This paper provides a mathematical analysis of a semi-classical signal analysis method applied to noisy signals, interpreting signals as potentials in a Schrödinger operator and examining its spectral properties in discrete settings.

Contribution

It offers a rigorous mathematical framework for understanding the semi-classical signal analysis method in the presence of noise, extending previous work to discrete and noisy cases.

Findings

Mathematical characterization of the method in noisy discrete signals

Insights into spectral properties of Schrödinger operators with noisy potentials

Potential robustness of the analysis method to noise

Abstract

Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this operator to analyze the signal. In this paper, we are interested in a mathematical analysis of this method in discrete case considering noisy signals.