## 4 Discussion
The EMD method that was applied to decompose the EEG was one the most novel of the multivariate versions; APTIT-MEMD [46] has been developed as an improvement to MEMD [64; 65], with the express purpose of coping with power imbalances and inter-channel correlations of multichannel signals, such as the EEG signal, and the method proposed by [52] was also used for the calculation of the mean spectral frequencies that mitigate the effect of some frequencies that have associated low values of power spectral density. However, as has been acknowledged by other authors, the mode-mixing problem continues to be a big issue for the analysis of multichannel signals such as EEG [17; 18; 47; 60]. For this reason, the physiological interpretation of changes related to the third and fourth intrinsic mode functions has to take this matter into consideration. However, it must also be acknowledged that different authors have questioned the limits generally established for the EEG bands, considering the findings that several oscillatory patterns can be present simultaneously and can modulate one another [9; 10; 13]. Considering the frequency range and topography of the overlapping patterns, it seems that alpha rhythm variability may be a possible explanation. Our results could be evidence of this fact and this physiological phenomenon could coexist with the effect of the mode mixing, but it appears impossible to separate them. The two methods used in this study proved to be equally informative for power spectral density estimation and the majority of the IMFs for mWf; nevertheless, careful attention must be paid to the first two IMFs. Previously, we demonstrated that the gamma band is a major point of disagreement for EEG broadband spectral analysis [56]. In this study, we offer evidence that, regardless of the decomposition process, the instantaneous frequency values offered by the Hilbert transform seem to impact positively on the high-frequency analysis and show a less overlapping percentage than the FFT method. It seems that the Hilbert transform and not the APTIT-MEMD provides the most probable explanation of the major capabilities of the HHT to assess the fastest EEG frequencies. Given the previous evidence, we recommend this approach because it produces a better frequency resolution as a result of the properties of the HHT method, and also because it does not demand the existence of linearity or stationarity on the EEG record. For this reason, this technique will be especially useful in conditions where these properties are absent and the EEG signal is truly disorganized or it varies from one person to another, such as in critically ill patients, where the previous establishment of frequencies band limits for a whole group could be a wrong assumption. Other research fields, such as brain-computer interface and machine learning, may benefit from this method, but more attention should be paid to physiological significances in those where the theta-alpha range is the main focus of investigation. The indices for broadband or narrow-band spectral analysis can be calculated from the multicomponent oscillatory modes of the EEG using both methods, and they can be interpreted by basing the analysis on their frequency ranges to assign their physiological meaning. Because of its strengths, the proposed methodology, based on an adaptive technique, could soon become an alternative to the classic spectral analysis of the EEG signals, particularly for the study of fast frequencies.