## 2 Proposed Methodology
### New Signal Combination Model with Four Common Methods
#### 2.2.1 CSP Using New Combinations of Signals  
The first proposed model increases the extraction of good distinctive features from the whole channel. In this model, new combinations of signals are created and applied individually in the classification. In this case, all of the electrodes are involved in extracting features. The model consists of four phases, as presented in Figure 5 and explained below:  
(1) Filtering data with Butterworth filter: In the first phase, using frequency filtering, noises and artifacts are removed with a filter bank. The domain of this filter bank is from the noise and artifact domains. EEG measurements are decomposed into nine filter banks of 4-8 Hz, 8-12 Hz, \(\ldots\), 36-40 Hz. All of the data are filtered by using a Butterworth filter of the 100 th order. Most researchers use the Butterworth filter for filtering [20,21]. (2) Creating new combinations of signals: The combination of two fixed filter banks creates a new combination of signals. Each fixed filter bank has a 4 Hz frequency range. For example, filter bank 5 starts with 20 Hz (lower band) and ends with 24 Hz (upper band). The new signal combination of filter banks 2 and 5 supports the 8-12 Hz and 20-24 Hz frequency ranges. The formula for new signals for all of the electrodes is calculated as:  
\[\mathrm{FB(i,j,m)=FB(i,m)+FB(j,m).\quad i,j=1\ldots 9,\quad\ m=1\ldots n.} \tag{3}\]  
where FB(i,j,m) represents the ith and jth filter banks of the mth channel, and n is the maximum number of electrodes used to record the data in the dataset. Therefore, the m  
Figure 5: Feature extraction (FE) from new hybrid signals using common spatial pattern (CSP). and i variables indicate the selected channel and the selected 4 Hz sized domain frequency (for example, m = 2 and i = 2 mean Channel 2 and the 8-12 Hz frequency range). (3) Using CSP as the spatial filter and feature extraction: The common spatial pattern algorithm [14; 15; 81; 82] is known as an efficient and effective EEG signal class analyzer. CSP is a feature extraction method that uses signals from several channels to maximize the differences between classes and minimize their similarities. This is accomplished by maximizing the variance of one class by minimizing the variance of another class. The CSP calculation is performed as follows:  
\[\mathrm{C}=\mathrm{EE^{{}^{\prime}}/trace}\Big{(}\mathrm{EE^{{}^{\prime}}} \Big{)} \tag{4}\]  
where C is the covariance of the normalized space of data input E, which provides raw data from a single imaging period. E is an N \(\times\) T matrix, where T is the number of electrodes or channels, and N is the number of samples in the channel. The apostrophe represents the transposition operator. Trace is a set of diagonal elements of x. The covariance matrix of both classes C\({}_{1}\) and C\({}_{2}\) is calculated from the average of several imaging periods of EEG data, and the covariance of the combined space Cc is calculated as follows:  
\[\mathrm{C_{c}}=\mathrm{C_{1}}+\mathrm{C_{2}} \tag{5}\]  
\(\mathrm{C_{c}}\) is real and symmetric and can be defined as follows:  
\[\mathrm{C_{c}}=\mathrm{u_{c}}\lambda_{\mathrm{c}}\mathrm{u_{c}^{{}^{\prime}}} \tag{6}\]  
where \(\mathrm{u_{c}}\) is a matrix of eigenvectors, and \(\lambda_{\mathrm{c}}\) is the diameter of the eigenvalue matrix. \[\mathrm{p}=\sqrt{\lambda^{-1}}\mathrm{u_{c}^{{}^{\prime}}} \tag{7}\]  
The variances in space are equalized by \(\mathrm{u_{c}^{{}^{\prime}}}\), and all eigenvalues of \(\mathrm{p\overline{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{   \mathrm{    }}}}}}}}}}}}}}\) are set to 1.