A time-varying Gaussian model for the complex-valued EEG spectrum during mental imagery tasks

Recent findings in neuroscience have shown that the spectral components of electroencephalogram (EEG) signals convey information regarding the mental task not only in their power but also in their phase. This calls for the utilization of complex-valued spectrum, instead of the commonly used power spectral density, in designing the brain computer interfaces. This paper studies the complex-valued spectrum of the EEG signal recorded during mental imagery tasks, and provides a statistical model for the EEG spectral components. Motivated by the results of a recent work by the authors, this paper proposes a time-varying noncircularly-symmetric Gaussian model for complex-valued EEG spectrum during a mental imagery trial. It will be shown that the mean of this Gaussian model is constant over time, whereas its variance and pseudo-variance follow an autoregressive conditional heteroscedastic (ARCH) model. The validity of this model is then verified using statistical tests.