Skip to main content
bioRxiv
  • Home
  • About
  • Submit
  • ALERTS / RSS
Advanced Search
New Results

Understanding Harmonic Structures Through Instantaneous Frequency

View ORCID ProfileMarco S. Fabus, View ORCID ProfileMark W. Woolrich, Catherine W. Warnaby, View ORCID ProfileAndrew J. Quinn
doi: https://doi.org/10.1101/2021.12.21.473676
Marco S. Fabus
1Nuffield Deparment of Clinical Neurosciences, University of Oxford, UK
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • ORCID record for Marco S. Fabus
  • For correspondence: marco.fabus@ndcn.ox.ac.uk
Mark W. Woolrich
2Department of Psychiatry, University of Oxford, UK
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • ORCID record for Mark W. Woolrich
Catherine W. Warnaby
1Nuffield Deparment of Clinical Neurosciences, University of Oxford, UK
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Andrew J. Quinn
2Department of Psychiatry, University of Oxford, UK
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • ORCID record for Andrew J. Quinn
  • Abstract
  • Full Text
  • Info/History
  • Metrics
  • Data/Code
  • Preview PDF
Loading

ABSTRACT

The analysis of harmonics and non-sinusoidal waveform shape in neurophysiological 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 harmonics structure in the FitzHugh-Nagumo model and the non-sinusoidal hippocampal theta oscillation in rat local field potential data. We further discuss how our definition helps to address mode splitting in EMD. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional and clinical roles of non-sinusoidal neural oscillations.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • katie.warnaby{at}ndcn.ox.ac.uk, mark.woolrich{at}ohba.ox.ac.uk, andrew.quinn{at}psych.ox.ac.uk

  • This research was funded in part by the Wellcome Trust [Grant numbers 203139/Z/16/Z, 106183/Z/14/Z, 215573/Z/19/Z]. For the purpose of open access, the authors have applied a CC-BY public copyright licence to any Author Accepted Manuscript version arising from this submission. Research was also supported by the NIHR Oxford Health Biomedical Research Centre, the New Therapeutics in Alzheimer’s Diseases (NTAD) study supported by UK MRC and the Dementia Platform UK (RG94383/RG89702), an EU European Training Network grant (euSSN; 860563), and the MRC Development Pathway Funding Scheme (award reference MR/R006423/1).

  • https://gitlab.com/marcoFabus/fabus2022_harmonics

  • http://shapegen.herokuapp.com/

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
Back to top
PreviousNext
Posted December 23, 2021.
Download PDF
Data/Code
Email

Thank you for your interest in spreading the word about bioRxiv.

NOTE: Your email address is requested solely to identify you as the sender of this article.

Enter multiple addresses on separate lines or separate them with commas.
Understanding Harmonic Structures Through Instantaneous Frequency
(Your Name) has forwarded a page to you from bioRxiv
(Your Name) thought you would like to see this page from the bioRxiv website.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Share
Understanding Harmonic Structures Through Instantaneous Frequency
Marco S. Fabus, Mark W. Woolrich, Catherine W. Warnaby, Andrew J. Quinn
bioRxiv 2021.12.21.473676; doi: https://doi.org/10.1101/2021.12.21.473676
Digg logo Reddit logo Twitter logo Facebook logo Google logo LinkedIn logo Mendeley logo
Citation Tools
Understanding Harmonic Structures Through Instantaneous Frequency
Marco S. Fabus, Mark W. Woolrich, Catherine W. Warnaby, Andrew J. Quinn
bioRxiv 2021.12.21.473676; doi: https://doi.org/10.1101/2021.12.21.473676

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
  • Tweet Widget
  • Facebook Like
  • Google Plus One

Subject Area

  • Neuroscience
Subject Areas
All Articles
  • Animal Behavior and Cognition (4086)
  • Biochemistry (8759)
  • Bioengineering (6478)
  • Bioinformatics (23339)
  • Biophysics (11747)
  • Cancer Biology (9147)
  • Cell Biology (13245)
  • Clinical Trials (138)
  • Developmental Biology (7413)
  • Ecology (11367)
  • Epidemiology (2066)
  • Evolutionary Biology (15086)
  • Genetics (10397)
  • Genomics (14008)
  • Immunology (9118)
  • Microbiology (22039)
  • Molecular Biology (8777)
  • Neuroscience (47356)
  • Paleontology (350)
  • Pathology (1420)
  • Pharmacology and Toxicology (2480)
  • Physiology (3703)
  • Plant Biology (8049)
  • Scientific Communication and Education (1431)
  • Synthetic Biology (2208)
  • Systems Biology (6015)
  • Zoology (1249)