Instantaneous frequency and wave shape functions (I)

TL;DR

This paper rigorously defines instantaneous frequency for nearly periodic waveforms and demonstrates how Synchrosqueezing can accurately determine it even for non-harmonic signals, with practical examples.

Contribution

It introduces a rigorous mathematical framework for instantaneous frequency of non-harmonic waveforms and extends Synchrosqueezing applications beyond harmonic signals.

Findings

Synchrosqueezing accurately estimates instantaneous frequency for a broad class of waveforms.

The paper provides real-life examples illustrating the advantages of non-harmonic waveform analysis.

A new theoretical foundation for instantaneous frequency in non-harmonic signals is established.

Abstract

Although one can formulate an intuitive notion of instantaneous frequency, generalizing "frequency" as we understand it in e.g. the Fourier transform, a rigorous mathematical definition is lacking. In this paper, we consider a class of functions composed of waveforms that repeat nearly periodically, and for which the instantaneous frequency can be given a rigorous meaning. We show that Synchrosqueezing can be used to determine the instantaneous frequency of functions in this class, even if the waveform is not harmonic, thus generalizing earlier results for cosine wave functions. We also provide real-life examples and discuss the advantages, for these examples, of considering such non-harmonic waveforms.