## 4 Discussion
If we pay attention to the mWf shown in Figure 5, we can conclude that IMF1 for our group showed values corresponding to the gamma band, IMF2 values corresponding to the beta-2 band, IMF5 values corresponding to the theta band and IMF6 values corresponding to the delta band, but for IMF3 values of frequencies of the alpha and beta-1 bands were detected, while for IMF4 the observed values belonged to the theta and alpha bands and both frequency ranges (IMF3 and IMF4) slightly overlapped (see also supplementary material). This pattern was observed for all EEG leads, mainly for parietal and occipital leads, and was also detected for the grand averages of the distribution of the mWf (Figure 3A) and the grand averages of the spectra of the IMFs in the group of subjects for the C3 EEG lead (Figure 3 B,C). Considering that the PSD normalized values (%) for IMF3 were almost twice as high as those observed for IMF4 (Figure 4), especially for the occipital and parietal leads, where the alpha rhythm is mainly localized in healthy subjects, this allows us to speculate that IMF3 better reflects the alpha spectral frequencies and could be considered to be mainly related to this classic band, whereas IMF4 could be more associated with the theta band. These results demonstrate one of the limitations of empirical mode decomposition, the so-called mode mixing, which consists in the appearance of different scales in an IMF, or when a signal with a similar scale appears in different IMF components. This has been reported and several methods have been proposed to mitigate its effects [18, 43, 47, 60]. Mode mixing is also evident in the grand mean of the instantaneous frequency distributions shown in Figure 4A. Analysis of the distributions of the instantaneous frequency values is one way of assessing this problem, previously proposed by another author who analyses the mode mixing problem in a decomposition obtained from the univariate EMD algorithm [43]. Our results show that the first and second IMFs are less affected by this problem, which justifies the consideration of these components by some authors for the study of fast EEG frequencies, especially for the gamma band range [2, 7, 8, 12, 43]. The improvement of feature extraction in EEG through HHT has resulted in the emergence of applications in fields such as brain-computer interface and machine learning [36, 37, 38, 39]. Nevertheless, the biological significance of the IMFs themselves and the influence of the mode-mixing problem on their neurophysiological interpretation has received less attention. This is a crucial problem that arises from antic assumptions, the supposition that all individuals have the same strict band limits regardless of their age, gender, or even physiological state, and the idea that the limits of all brain oscillators cannot be overlapped between themselves. The limitations of the FFT influenced these assumptions, imposed on the researchers specifically because the discrete frequency estimations are multiples of a spectral resolution and as a consequence of the Heisenberg uncertainty principle [50]. The HHT offers a possible solution: a new way to interpret the spectral properties of the EEG signal. However, the mode-mixing problem frequently interferes with this interpretation, and more critically the EEG signal seems to be more affected than other signals, such as heart rate tachogram [53; 61; 62]. Another interesting piece of evidence is that mode mixing does not affect all IMFs equally; IMFs 3 and 4, related to classical alpha and theta band activities, were more overlapped than the others independently of the employed mode decomposition technique [33; 51; 53; 63]. Important to note is the topography of the mode mixing between IMFs 3 and 4, more evident in the parietal and occipital areas, as was mentioned and depicted before (Figure 5). In the present study, we applied different strategies to mitigate mode mixing.