For every subject, power spectral density from 1 to 100 Hz was estimated for each of the 100 epochs of five seconds, for each electrode configuration. The following statistical analysis was done independently for each subject. To enable paired comparisons of the power spectra, the signals were grouped based on the quad electrode configuration. For example, small electrodes 1, 2, 9, and 10 were compared to two paired electrodes (1 shorted to 2, and 9 shorted to 10) and one quad electrode (1, 2, 9, and 10 shorted together) (see figure 3 ). For each set of four small electrodes, the power spectra were estimated by using the Fourier periodogram which is the data-analogue of the spectrum defined on the fundamental frequencies. Since periodograms are quite noisy, they need to be smoothed in order to obtain a mean-squared consistent estimator [34 (link)]. In some applications, it is more convenient to use log periodograms (rather than periodograms) because their variance is approximately constant across frequencies. Here, log periodograms were calculated and smoothed across frequencies using a moving average filter with a span of 5 data points (0.5 Hz). For each set of two pair electrodes, the two log periodograms were averaged and smoothed using a span of 10 data points (1 Hz). For the quad electrodes, the log periodograms were used without averaging and were smoothed using a span of 20 data points (2 Hz).
Thus, for each configuration, a set of 1600 log periodograms was obtained (16 signals × 100 epochs). To explore structures, patterns, and features in the sample of periodograms’ curves, we followed Ngo et al and constructed a functional box plot (FBP) [35 (link)], a generalization of the classical pointwise boxplot. For each curve, a modified band depth (MBD) value is computed [36 (link)]. This indicates whether or not a curve is covered by many pairs of curves in the data. Based on the ranks of MBD values, the FBP provides descriptive statistics, such as the functional median curve, which has the highest MBD value.
Thus, for each configuration, a set of 1600 log periodograms was obtained (16 signals × 100 epochs). To explore structures, patterns, and features in the sample of periodograms’ curves, we followed Ngo et al and constructed a functional box plot (FBP) [35 (link)], a generalization of the classical pointwise boxplot. For each curve, a modified band depth (MBD) value is computed [36 (link)]. This indicates whether or not a curve is covered by many pairs of curves in the data. Based on the ranks of MBD values, the FBP provides descriptive statistics, such as the functional median curve, which has the highest MBD value.
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