Defining the filter parameters for phase-amplitude coupling from a bispectral point of view

Coen S. Zandvoort*, Guido Nolte

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


BACKGROUND: Two measures of cross-frequency coupling are phase-amplitude coupling (PAC) and bicoherence. The estimation of PAC with meaningful bandwidth for the high-frequency amplitude is crucial in order to avoid misinterpretations. While recommendations on the bandwidth of PAC's amplitude component exist, there is no consensus yet. Theoretical relationships between PAC and bicoherence can provide insights on how to set PAC's filters.

NEW METHOD: To illustrate this, PAC estimated from simulated and empirical data are compared to the bispectrum. We used simulations replicated from earlier studies and empirical data from human electro-encephalography and rat local field potentials. PAC's amplitude component was estimated using a filter bandwidth with a ratio of (1) 2:1, (2) 1:1, or (3) 0.5:1 relative to the phase frequency.

RESULTS: For both simulated and empirical data, PAC was smeared over a broad frequency range and not present when the estimates comprised a 2:1- and 0.5:1-ratio, respectively. In contrast, the 1:1-ratio accurately avoids smearing and results in clear signals of cross-frequency coupling. Bicoherence estimates were found to be essentially identical to PAC calculated with the recommended frequency setting.

COMPARISON WITH EXISTING METHOD(S): Earlier recommendations on filter settings of PAC lead to estimates which are smeared in the frequency domain, which makes it difficult to identify cross-frequency coupling of neural processes operating in narrow frequency bands.

CONCLUSIONS: We conclude that smearing of PAC estimates can be avoided with a different choice of filter settings by theoretically relating PAC to bicoherence.

Original languageEnglish
Article number109032
Pages (from-to)1-12
Number of pages12
JournalJournal of Neuroscience Methods
Issue number350
Publication statusPublished - 15 Feb 2021

Bibliographical note

Copyright © 2020 The Author(s). Published by Elsevier B.V. All rights reserved.


  • Cross-frequency coupling
  • Bicoherence
  • Phase-amplitude coupling


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