Signal Analysis by Expansion Over the Squared Eigenfunctions of an Associated Schr\"odinger Operator

TL;DR

This paper presents a novel signal analysis technique that interprets pulse signals as potentials of Schrödinger operators, using their discrete spectrum for analysis, demonstrated on arterial blood pressure signals.

Contribution

It introduces a new method for signal analysis based on spectral decomposition of Schrödinger operators, linking signal processing with quantum mechanics concepts.

Findings

Effective analysis of arterial blood pressure signals

Spectral representation captures signal features

Method shows promise for biomedical signal analysis

Abstract

This article introduces a new signal analysis method. The main idea consists in interpreting a pulse-shaped signal, after multiplying it by a positive parameter, as a potential of a Schr\"odinger operator and representing this signal with the discrete spectrum of this operator. We present some results obtained in the analysis of the arterial blood pressure with this method.