Understanding Harmonic Structures Through Instantaneous Frequency | IEEE Journals & Magazine | IEEE Xplore

Understanding Harmonic Structures Through Instantaneous Frequency


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 ...Show More

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.
Published in: IEEE Open Journal of Signal Processing ( Volume: 3)
Page(s): 320 - 334
Date of Publication: 10 August 2022
Electronic ISSN: 2644-1322
PubMed ID: 36172264

Funding Agency:


References

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