Electroencephalogram (EEG) recordings of brain activities can be processed in order to augment the brain's cognitive, sensory, or motor functionality. A representative, yet analytically tractable, model is essential to EEG processing. Several studies have examined different statistical models for EEG power spectrum. But recent studies have shown that not only the power, but also the phase of the spectrum, carries relevant information on brain activities. As a result, this paper focuses on the complex-valued spectrum of EEG, and proposes a general non-circularly-symmetric multivariate Gaussian model for this spectrum. This simple model can encapsulate the information in both power and phase of the spectrum, and its validity for EEG data has been verified using standard statistical tests.
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