Envelope Analysis of the Human Alpha Rhythm Reveals EEG Gaussianity

Objective:
To assess the Gaussianity of the human alpha rhythm using the envelope signal and the coefficient of variation of the envelope (CVE).
Methods:
Envelope analysis relies on the fact that the CVE for Gaussian noise is
$\sqrt{(4-\pi)/\pi }\approx 0.523$
. CVE can thus be used as a hallmark to detect Gaussianity, and any significant deviation from Gaussianity can be linked to synchronous neural dynamics. We applied envelope analysis to EEG and iEEG public databases.
Results:
The human alpha rhythm can be characterized either as a synchronous or as a Gaussian signal based on the value of its CVE. Furthermore, Fourier analysis showed the canonical spectral peak at
$\approx$
10[Hz] is present in both the synchronous and Gaussian cases, thus demonstrating this same peak can be produced by different underlying neural dynamics.
Conclusion:
Human EEG can be classified using envelope parameters. This study confirms the original interpretation of Adrian regarding the origin of the alpha rhythm but also opens the door for the study of Gaussianity in brain dynamics.
Significance:
Envelope analysis constitutes a novel complement to Fourier-based methods for neural signal analysis relating amplitude modulations (CVE) to signal energy. These results suggest a broader interpretation for event-related synchronization/desynchronization (ERS/ERD) may be needed.