Understanding harmonic structures through instantaneous frequency

Marco S. Fabus*, Mark W. Woolrich, Catherine W. Warnaby, Andrew J. Quinn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Downloads (Pure)

Abstract

The analysis of harmonics and non-sinusoidal waveform shape in time-series data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonic structures in shallow water waves, the FitzHugh-Nagumo neuronal model, and the non-sinusoidal theta oscillation in rat hippocampus local field potential data. We further discuss how our definition helps to address mode splitting in nonlinear time-series decomposition methods. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional roles of non-sinusoidal oscillations.
Original languageEnglish
Pages (from-to)320-334
Number of pages15
JournalIEEE Open Journal of Signal Processing
Volume3
Early online date10 Aug 2022
DOIs
Publication statusPublished - 24 Aug 2022

Keywords

  • Electrophysiology
  • Empirical Mode Decomposition
  • Harmonic Analysis
  • Hilbert Transform
  • Instantaneous Frequency

Fingerprint

Dive into the research topics of 'Understanding harmonic structures through instantaneous frequency'. Together they form a unique fingerprint.

Cite this