## 4 Discussion  
Improvements in EEG feature extraction techniques using the Hilbert-Huang transform (HHT) have led to many applications in various fields, but the biological significance of IMFs and the influence of mode mixing on their interpretation have received insufficient attention, revealing limitations arising from previous assumptions about band boundaries when analyzing brain oscillators. The results obtained using the two methods in this study showed that the first six intrinsic mode functions (IMFs) extracted from the EEG of the 19 studied scalp positions contained frequencies that approximately corresponded to the range from 1.5 to 56 Hz, considering the observed mean values of the mean weighted frequencies (mWf) (Figure 5). This range corresponds to the expected frequencies of the EEG from the classical delta to the gamma bands. The power spectral density estimates expressed in normalized units (%) of the IMFs did not show significant differences between the methods for clinical purposes considering the agreement analysis (Table 1 and Figure 8) [56]. The agreement analysis shows that a significant bias exists when the zero line (line of equality) falls outside the confidence interval. However, only biologically, analytically or clinically relevant criteria can determine whether the agreement interval is appropriate or too wide for the intended purpose. This method has previously been used to evaluate quantitative EEG methods [58] and has also been used to determine the agreement between the HHT and FFT-based methods for broadband EEG spectral analysis [53]. However, it has not been previously reported for IMF-based quantitative EEG analysis. Regardless of the results of the ANOVA  
Figure 8: Agreement analysis between HHM and FFT methods for the mean frequency and the NU (%) of PSD values during functional resting state of relaxed wakefulness with eyes closed. The Y axes represent the differences between HHT and FFT values (HHT-FFT) and the X axes the mean of both methods (HHT + FFT/2). Red line—mean of differences; black lines—limits of the agreement (mean \(\pm\)1.96 \(\times\) standard deviation); blue discontinued line— linear trend of the differences; black discontinued line—zero level. LoAu—Upper agreement limit; LoAi—lower agreement limit; IMF—intrinsic mode function. test for mWf, if we look at the individual differences between the methods for each subject, as reflected in the agreement analysis, a new result emerges, showing the first two IMFs as the major dissimilarity between the methods. The differences in the mWf can be attributed to the fact that the HHT method has a higher instantaneous frequency resolution than the FFT method, as noted by other authors [59, 60], and to the fact that the Fourier transform has more constant weighted frequencies than the Hilbert transform, which allows the frequency and amplitudes to vary over time [21]. An example of this is the results obtained for EEG lead C3 (Figure 4). It is impossible to obtain a grand average of the distributions of discrete frequencies calculated using the FFT method, because these frequencies are multiples of the predefined spectral resolution and remain constant for all IMFs derived from the EEG leads of all subjects. As a result, only the FFT spectra of the IMFs were plotted (Figure 4B,C). Some authors have suggested that the first IMFs decomposed from the EEG using multivariate empirical mode decomposition could be associated with classical EEG bands [15, 18, 41, 43]. IMF1 would correspond to the gamma band, IMF2 to the beta band, IMF3 to the alpha band, IMF4 to the theta band and IMF5 and IMF6 to sub-bands of the delta band [43]. Our results are not consistent with this.