## 3 EEG Analysis  
In this section, the processing steps are described which helps cleaning the signals from additional perturbations in order to enhance the SNR and give us information over the neurophysiological effects of perception, interpretation and cognition. For a complementary overview of the neural activity [57], we investigate not only the temporal responses (ERPs), but also the oscillations in the spectral domain (Power spectral density, PSD), as well the neural modulations given by (De)Synchronization (ERD/ERS) in order to observe how the frequency oscillations vary in time, which are investigated in more detail with Event-Related Spectral Perturbation (ERSP) which can capture all together the modulations within the entire frequency spectrum over time. 1. Bad channels rejection (Participant-specific bad channels rejection and low quality channels rejection)--Firstly, bad quality data was removed from further analysis, such as bad signal quality due to poor conductance, e.g., signal amplitude > 300 uV. Further, channels were checked for variance dropping to zero and removed if positive (criterion: variance < 0.5 in more than 10% of trials [58; 59]. 2. Filtering--we applied low-pass and high-pass filtering. For lowpass filtering, used for anti-aliasing, we applied the Chebyshev type II filter of order 10 with 42 Hz pass-band edge frequency and 3 dB ripple, and a 49 Hz stopband with 50 dB attenuation. The high-pass filter, used to reduce drifts, was applied with a 1 Hz FIR filter of order 300, using least-squares error minimization and reverse digital filtering with zero-phase effect, such as not to induce phase delays. 3. Artifact rejection--For the purpose of rejecting non-EEG origin components (ocular, muscular, cardiovascular, etc. ), Independent Component Analysis (ICA) with Multiple Artifact Rejection Algorithm (MARA) based on feature selection [60] were used. Figure 4: Experimental paradigm and timing: fixation period of 500 ms, trial of 1000/750/500 ms for blocks, and relaxation period of 700 ms. Segmentation--Data was segmented in epochs, where one epoch corresponds to one stimulation sequence. 5. Epochs rejection--Noisy trials were removed based on a variance criterion, such as the ones greater or equal then a trial threshold per channels (where in 20% of the channels have excessive variance). Further, artifactual trials were rejected based on max-min criterion, such as the difference between the maximum and minimum peak should not exceed a threshold, e.g., 150 \(\mu\)V.
6. Baseline correction--For each epoch, the mean of the last hundreds of ms from the attentional period is subtracted from the epoch, either in the time or frequency domains, aiming at diminishing the background neural noise activity [61]. 7. Grand Average (GA)--All trials have been averaged over all participants for neurophysiological interpretation, and investigated in the temporal and frequency domains. Scalp maps distributions of the brain signals will also be presented, where a shading method based on linear interpolation between neighbor channels is used to get smooth plots (available via BBCI Toolbox, [55]). 1. Event-Related Potential, ERP analysis--For ERP analysis, the temporal signals are investigated and averaged on all signals over all participants. For baseline correction, the last 100 ms are used from the attentional period. 2. Signed and squared point biserial correlation coefficient measure (signed \(r^{2}\))--For details on the association strength between the brain responses for different perceptions, the signed and squared point biserial correlation coefficient (signed \(r^{2}\)) [62] is computed separately for each pair of channel and time point (\(x\)), over all epochs, as in [63], being proposed by [64] (see Equation (3)). 3.