A novel wave decomposition for oscillatory signals

TL;DR

This paper introduces a new wave decomposition method for oscillatory signals, modeling them as multicomponent FMM with Gaussian noise, and demonstrates its effectiveness in neuroscience applications.

Contribution

It proposes a novel AM-FM decomposition approach with theoretical properties and practical applications in neuroscience, improving over traditional Fourier methods.

Findings

The method accurately models neuron synapse signals.

The decomposition provides new insights into oscillatory dynamics.

The approach is robust to noise and complex signals.

Abstract

Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct physiological meaning, they are not useful in practice as a result of the parameter adjustment complexity and the presence of noise. In this paper, a signal plus error model is proposed to analyze oscillations, where the signal is a multicomponent $FMM$ and the noise is assumed Gaussian. The signal formulation is also a novel decomposition approach in AM-FM components, competing with Fourier and other decompositions. Several interesting theoretical properties are derived including the Ordinary Differential Equations describing the signal. Furthermore, the usefulness in real practice is demonstrate to analyze signals associated to neuron synapses and by addressing other questions in Neuroscience.