## 2 Materials and Methods
### Proposed Methodology for Signal Processing
#### 2.3.2 Analysis Using the Coefficient of Determination r\({}^{2}\)  
The analysis is based on the calculation of the coefficient of determination r\({}^{2}\) and on the visual inspection of the EEG spectrum. r\({}^{2}\) is the square of the correlation coefficient and represents the coefficient of determination between the two parameters that form [PERSON]'s correlation coefficient r. These parameters being the covariance of the series and the product of their standard deviations. The statistical index r\({}^{2}\) has values between 0 and 1 and can be considered as an index that shows how different two signals are (at a certain frequency/channel). The difference between the signals can be explained by the fact that they come from different sources (in our case they correspond to different tasks, motor imagery and relaxation). A value of r\({}^{2}\) close to 1 indicates a good discrimination of sensorimotor rhythms. The coefficient r is calculated as follows  
\[\mathrm{r}=\frac{\sum_{i=1}^{n}\left(\mathrm{x_{i}}-\overline{\mathrm{X}} \right)\left(\mathrm{y_{i}}-\overline{\mathrm{Y}}\right)}{\sqrt{\sum_{i=1}^{n }\left(\mathrm{x_{i}}-\overline{\mathrm{X}}\right)^{2}}\sqrt{\sum_{i=1}^{n} \left(\mathrm{y_{i}}-\overline{\mathrm{Y}}\right)^{2}}} \tag{2}\]  
where X = x\({}_{1}\), x\({}_{2}\),..., x\({}_{n}\) and Y = y\({}_{1}\), y\({}_{2}\),..., y\({}_{n}\) are the measured values, and \(\overline{\mathrm{X}},\overline{\mathrm{Y}}\) are the sampling averages of the respective series. After each training paradigm, the acquired signals are analyzed to decide whether or not they were recorded correctly in terms of MI sensorimotor discrimination. Figure 8 shows the values of the coefficient of determination calculated for the signal corresponding to MI of the movement of the left hand vs. relaxation, and Figure 9 presents the values for the coefficient of determination calculated for the signal corresponding to the MI of the movement of the right hand vs. relaxation. Figure 7: Multiresolution UWT decomposition for EEG signal. Figure 8: Coefficient of determination calculated for the signal corresponding to MI of the left hand vs. relaxation. Figure 9: Coefficient of determination calculated for the signal corresponding to the MI of the right hand vs. relaxation. The channels of interest in the case of motor imagery of the left hand are C4, CP4 and P4; for the signals recorded by us the best value of r\({}^{2}\) was obtained on the C4 channel, and the best values are obtained on channels of interest, CP4 and C4. It is also observed that the highest value of r\({}^{2}\) was about 0.45. For the right hand, it is observed that we obtained higher values for r\({}^{2}\) on channels 1 (CP3), 3 (P3) and 4 (C3) in the frequency range 14-22 Hz. On these channels, the maximum value of r\({}^{2}\) was about 0.3. Analyzing the signals from all subjects in this way, we prepared Table 1. For the article in Table 1, we present the results for 5 subjects (relevant summary). This table provides information for 45 subjects (in full form) because they only discriminated the sensorimotor rhythms from the 60 who performed the experiment. Table 1 contains information on the frequency of occurrence of MI sensorimotor rhythms and the corresponding channels, as well as the maximum value of the statistical index r\({}^{2}\). At this stage the acquisition of EEG signals is presented. Acquiring signals is a very important step, even decisive, in terms of success and results of the next stages, requiring significant resources of time and volunteers willing to perform experiments. The research on the acquired data is much more efficient, knowing all the details and conditions in which the recordings were made but also the opinions of the volunteers and their statements about the experiment and whether or not they managed to imagery their movement, this being a no just easy to do. A small, viable database containing EEG signals was recorded during MI hand movement from 45 subjects.