Instantaneous frequency and amplitude identification using wavelets: Application to glass structure

TL;DR

This paper introduces a wavelet-based method for rapidly extracting instantaneous frequency and amplitude from complex signals, enabling detailed analysis of material structures with high resolution.

Contribution

It presents a modified Morlet wavelet and a stationary-phase approximation for improved high-resolution analysis of oscillatory signals.

Findings

Successfully applied to a disordered material's structural correlation function

Revealed previously undetected features in the material analysis

Demonstrated high-resolution extraction of signal modulations

Abstract

This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which is a modification to the well-known Morlet wavelet to allow analysis at high resolution. In order to interpret the CWT of a signal correctly, an approximate analytic expression for the CWT of an oscillatory signal is examined via a stationary-phase approximation. This analysis is specialized for the new wavelet and the results are used to construct expressions for the amplitude and frequency modulations of the components in a signal from the transform of the signal. The method is tested on a representative, variable-frequency signal as an example before being applied to a function of interest in our subject area - a structural correlation function of a disordered material - which immediately reveals previously undetected features.