Modeling electroencephalography (EEG) in the frequency domain and the time domain




Shi, Chao

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One of the important problems in neuroscience is determining the reliability of repeated EEG recordings over time. Quantifying the intra-individual stability/ variability in the recordings allows researchers to test for the effects of retention or learning for different types of subjects, as well as to examine the influence of external factors. In this dissertation, we consider models for R repeated EEG time series in both the time and frequency domains. We develop methodology to assess and quantify the reliability of the series.

In the frequency domain, we propose three spectral closeness coefficients that quantify the closeness of the R spectra at individual frequencies and across specified frequency bands. These closeness measures are computed from the smoothed periodograms of the R EEG time series. Under certain assumptions, we derive the exact distribution of the spectral closeness coefficients scc1 and scc2 and compare their performance in terms of mean squared error. Based on the results, we propose a third closeness measure scc3 and investigate its properties across the entire frequency band [0:5; 30) Hz through a simulation study.

In the time domain, we propose a sum-of-sinusoids model for the EEG time series. We develop algorithms to estimate the model parameters including the amplitudes, frequencies, phases, and the number of sinusoidal components. To compare the R series, we construct a likelihood ratio test (LRT) for testing the null hypothesis that all R series have the same parameters. The p-value of the LRT provides a measure of closeness of the R series based on the underlying parametric model and may be used to cluster the R series. We extend the single-channel model to the multi-channel case with suitable assumptions on the correlation structure in the spatial and time domains.

We illustrate the performance of the proposed methods on two real EEG datasets. The results based on the spectral closeness coefficients show spectral features of high reliability that may be used as an input for a brain-computer interfacing (BCI) system. Using the LRT based on the sumof-sinusoids model, we can determine which of the R series on a single subject are similar, and also quantify the differences between subjects.


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EEG, likelihood ratio test, spectral closeness coefficient, sum-of-sinusoids model



Management Science and Statistics