## 4 Experimental Studies
### Results  
The classification results are evaluated and compared by utilizing the kappa coefficient, which takes the value 0 for a random classifier and 1 for a perfect classifier that consistently correctly classifies. The estimation of kappa coefficient is computed utilizing the equation below:  
\[K=\ \frac{P_{0}-P_{e}}{1-P_{e}} \tag{12}\]  
where \(P_{0}\) denotes the classification accuracy and \(P_{e}\) denotes the hypothetical accuracy of a random classifier on the same data. \[A=\frac{(P_{0}-0.25)}{1-0.25} \tag{13}\]  
In above equation, we consider the value for \(P_{e}\) = 0.25. The final proportion of execution of a given algorithm is the maximum value of the kappa value from the computed time-course. The Fisher ratio is performed for obtaining the user specific band. After analysing the EEG signals and comparing it with the time domain parameters, the most dominant frequency band and timing is identified by using the Fisher ratio of the time domain parameter. The FDA type F-score has  
Figure 2: The time course of a single trial in the Brain Control Interface (BCI) competition IV dataset 2a. been used for the subject specific band. [PERSON]'s discriminant analysis is performed to identify both the dominant frequency band and timing for multiple class classification. It estimates the time and frequency areas for extracting the features of TDP with respect to subject. While the user specific and subject specific band are individually applied, they are also applied together as the proposed system. Different frequency intervals and time intervals are observed to identify the most optimum intervals. To identify the best time interval, they are examined with the feature extraction techniques and feature reduction while using PCA. After this, [PERSON]'s LDA was used as a classifier. Figure 3 shows an original EEG signal. The electroencephalogram (EEG) is the recording of the electrical movement of the brain from the scalp. The recorded waveforms indicate the cortical electrical movement. EEG activity is quite small and they are measured in terms of microvolts. Figure 4 shows a band-pass filter is used to display frequencies that are either too low or too high, making it easy to pass frequencies within a certain range. Band-pass filters can be created by stacking a low-pass filter at the end of a high-pass filter. Figure 4: Band pass filter. Figure 3: Original Electro-Encephalo-Graphy (EEG) signal. The Daubechies wavelets are a family of orthogonal wavelets and identify discrete wavelet transform. The coefficients of a one-dimensional signal are reconstructed and they are shown in Figure 5. The brain has five distinctive categories of brain waves; Gamma, Theta, Delta, Alpha, and Beta brain waves. Figure 6 shows the frequency of brain waves. Gamma wave occurs maximum frequency at 12.00 Hz. Beta wave occurs maximum frequency at 6.00 Hz. Alpha wave occurs maximum frequency at 3.00 Hz. Theta wave occurs maximum frequency at 1.00 Hz. Delta wave occurs Maximum frequency at 1.00 Hz. Band pass filter is utilized for EEG signal denoising. Figure 7 shows the denoised EEG signal. Figure 5: EEG brain waves. Figure 6: Frequency in EEG brain waves. This work performs a ten-fold cross validation. The TDP is utilised for identifying the optimum frequency band and timing during the training process. The band is subject to by-pass filtering to remove undesirable noises. Table 1 gives the range of the optimum frequency band and timing. In the user specific band, the feature extraction is performed by all three discussed feature extraction techniques, which are TDP, FFT, and PCA in the BCI system. As every individual subject has different frequency and timing bands, the dominant bands must also be identified for the individual subject. Accordingly, we select the frequency band and the timing using the Fisher ratio of the time domain parameter.