## 2 Materials and Methods
### Estimation of the PSD of the IMFs Using the FFT Method and Spectral Indices (FFT)  
The power spectrum was calculated for each extracted IMF of every EEG lead using the Welch periodogram method, with the Matlab function \"pwelch.m\", a window of 512 samples, a 50% overlap, a Hamming window, and 2000 samples for the FFT. The spectral resolution was 0.1 Hz. The absolute spectral power (\(\rm{P_{imf}}\)) of each IMF (n) was calculated for the whole-time duration of the EEG segments (60 s) from the corresponding IMFs, following the expression:  
\[\rm{P_{imf_{n}}}=\sum_{i=min}^{max}P_{i}; \tag{2}\]  
where P is the discrete power values of the spectra obtained for each spectral resolution multiples (i) of each IMF (n),'min' represents the lower limit value of the spectral range to consider (1 Hz), and'max' is the upper limit (70 Hz in this study) [50; 51].  
The spectral relative power (NU) of each IMF (n) expressed in normalized units (%) was calculated as:  
\[\rm{NU_{imf_{n}}}=\frac{P_{imf_{n}}}{P_{L}}\times 100; \tag{3}\]  
where \(\rm{P_{imf}}\) is the absolute power of each IMF (n), and Pt is the sum of the absolute power of the six IMF Welch spectra for the corresponding EEG lead (L) [50; 51].  
The mean weighted frequency (\(\rm{mWf_{imf}}\)) [40] of each IMF (n) spectra, expressed in Hz, was calculated using the expression:  
\[\rm{mWf_{imf_{n}}}=\sum_{i=min}^{max}\frac{f_{i}\times P_{i}}{P_{imf_{n}}}\ \ ; \tag{4}\]  
where f is the discrete spectral frequency and P is the corresponding discrete spectral power for each one of the spectral resolution multiples (i). \(\rm{P_{imf}}\) is the absolute power calculated for the spectrum of the corresponding IMF (n),'min' is the lower value of the spectral range (1 Hz), and'max' is the upper limit (70 Hz) [52; 53].  
For estimation of the PSD of the IMFs using the HHT method and spectral indices (HHT), the Hilbert transform was applied to each extracted IMF of every EEG, leading to the creation of analytical functions, referred to here as Z(t), that can be written as:  
\[\rm{Z(t)}=\rm{X(t)}+iY(t); \tag{5}\]  
where X(t) is the input time series (the IMF in this case) and iY(t) is the Hilbert transform of X(t) [19]. The instantaneous values of power and frequency can then be obtained using the following expressions:  
\[\rm{P(t)}=\left[X(t)^{2}+Y(t)^{2}\right]; \tag{6}\]  
\[\rm{\omega(t)}=\frac{d\theta(t)}{d(t)}; \tag{7}\]  
where P(t) is the instantaneous energy power, \(\theta\)(t) is the phase, and \(\rm{\omega(t)}\) is the instantaneous frequency. Spectral indices were then calculated for the 60 s EEG segments, from which the corresponding IMFs were extracted [19, 51]. The absolute spectral power (P\({}_{\text{imf}}\)) of each IMF (n) was calculated using the expression:  
\[\text{P}_{\text{imf}_{n}}=\sum_{\text{i=1}}^{\text{i=12000}}\text{IP}_{\text{i}}; \tag{8}\]  
where IP is the consecutive values of instantaneous power obtained from each sample (i) of the input signal; in this case, the IMF with 12,000 samples (60 s of EEG recording at 200 Hz of sampling frequency) [50]. The spectral relative power (NU) of each IMF (n) expressed in normalized units (%) was calculated as:  
\[\text{NU}_{\text{imf}_{n}}=\frac{\text{P}_{\text{imf}_{n}}}{\text{P}_{\text{tL }}}\times 100; \tag{9}\]  
where P\({}_{\text{imf}}\) is the absolute power of each IMF (n), and Pt is the sum of the absolute power of the six IMF obtained from the corresponding EEG lead (L). The mean weighted frequency (mWf\({}_{\text{imf}}\)) of each IMF (n) expressed in Hz was calculated, also following the recommendations of a previous author [40] using the expression:  
\[\text{mWf}_{\text{imf}_{n}}=\sum_{\text{i=1}}^{\text{i=12000}}\frac{\text{If} _{\text{i}}\times\text{IP}_{\text{i}}}{\text{P}_{\text{imf}_{n}}}; \tag{10}\]  
where If represents the consecutive instantaneous frequencies and IP the corresponding values of instantaneous powers obtained from each sample (i); in this case, 12,000 samples. P\({}_{\text{imf}}\) is the absolute power calculated for the corresponding IMF (n).