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The bispectrum and its relationship to phase-amplitude coupling.
Christopher K Kovach1, Hiroyuki Oya1, Hiroto Kawasaki1
1Department of Neurosurgery, University of Iowa Carver College of Medicine, Iowa City, IA, USA.
Neuroimage
|February 27, 2018
Summary
The bispectrum, a tool for analyzing nonlinear biological signals, is closely related to phase-amplitude coupling (PAC) measures. Understanding this connection reveals limitations in current PAC methods and offers a framework for better signal analysis.
Area of Science:
- Neuroscience
- Signal Processing
- Biophysics
Background:
- Biological signals often exhibit non-Gaussian properties due to nonlinear physiological systems.
- Polyspectra, particularly the bispectrum, analyze higher-order moments for cross-frequency dependence in non-Gaussian signals.
- Phase-amplitude coupling (PAC) is a recent focus in EEG analysis for cross-frequency dependence.
Purpose of the Study:
- To demonstrate the close relationship between the bispectrum and popular phase-amplitude coupling (PAC) measures.
- To highlight the limitations of conventional PAC measures when viewed as smoothed bispectral estimators.
- To propose guidelines for interpreting cross-frequency coupling using bispectral statistics.
Main Methods:
- Relating popular PAC measures to smoothed versions of the signal bispectrum.
- Analyzing the properties of conventional PAC measures, including bias and symmetry.
- Comparing information preserved in bispectral estimators versus smoothed PAC measures.
Main Results:
- Conventional PAC measures are fundamentally smoothed bispectral estimators with unfavorable bias and symmetry properties.
- Information critical for distinguishing oscillations from transient features is obscured by smoothing in PAC measures.
- Bispectral estimators preserve information that PAC measures smooth over, aiding in distinguishing signal features.
Conclusions:
- A unified framework for interpreting the bispectrum and other higher-order spectra is presented.
- This framework enhances the identification of nested oscillations and transient phenomena in biological signals.
- The study provides guidelines for accurately assessing cross-frequency coupling and its origins.
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