## 6 EEG Signal Pre-Processing and Feature Extraction
### EEG Signals Feature Extraction  
Nonlinear features are commonly used in emotion recognition research utilizing EEG signals. When using datasets like DEAP, the correlation between electrode voltage and reported emotions is often weak, as indicated by statistical analysis [79]. Therefore, incorporating nonlinear features is essential in EEG-based emotion recognition systems. After determining the appropriate frequency band and the number and placement of sensors, the most frequently used feature is power spectral density. In some studies, power density is employed to create a topographical representation of brain signals, considering specific sensor numbers and frequency ranges within a selected window size, as illustrated in the heat map in Figure 7.  
\begin{table}
\begin{tabular}{c c} \hline
**Signal Band** & **Frequency Range** \\ \hline Delta & \textless{}3 Hz \\ \hline Theta & 4–7 Hz \\ \hline Alpha & 8–12 Hz \\ \hline Beta & 13–30 Hz \\ \hline Gamma & \textgreater{}30 Hz \\ \hline \end{tabular}
\end{table}
Table 3: EEG frequency bands.  
Figure 7: EEG topography heat brain image.  
Generally, EEG features can be classified into three categories: time domain, frequency domain, and time-frequency domain features. Time domain features including various statistical measures such as the mean, standard deviation, range, skewness, kurtosis, as well as Hjorth parameters including activity, mobility, and complexity [105; 106; 107]. These standard statistical features are described below:  
* Mean: \[\text{Mean}(x)=\frac{1}{n}\sum_{t=1}^{n}x(t)\] (1)
* Standard Deviation: \[\text{Std}(x)=\frac{1}{n}\sum_{t=1}^{n}\left(x(t)-\text{Mean}(x)\right)\] (2)
* Range: \[\text{Range}(x)=\text{max}\left(x\right)-\text{min}\left(x\right)\] (3)
* Skewness: \[\text{Skewness}(x)=\text{Mean}(\left(x-\text{Mean}(x)\right)^{3})\] (4)
* Kurtosis: \[\text{Kurtosis}(x)=\frac{\text{Mean}(\left(x-\text{Mean}(x)\right)^{4})}{ \text{Std}(x)^{4}}\] (5)
* Hjorth parameter-activity: \[\text{Activity}(x)=\text{Std}(x)^{2}\] (6)
* Hjorth parameter-mobility: \[\text{Mobility}(x)=\sqrt{\frac{\left(\text{Std}(\frac{dx}{dt})\right)^{2}}{ \left(\text{Std}(x)\right)^{2}}}\] (7)
* Hjorth parameter-complexity: \[\text{Complexity}(x)=\sqrt{\frac{\text{Mobility}(\frac{dx}{dt})}{\text{Mobility}(x)}}\] (8)  
In this context, \(x(t)\) denotes the raw EEG signal comprising \(n\) samples. The described features are commonly known as statistical features. Frequency domain features, on the other hand, are derived from the frequency components extracted from the original signal. The key frequency features include power, power ratio, and power spectral density, which can be summarized as follows:  
* Power spectral density: \[\text{PSD}(x)=\lim_{T\rightarrow\infty}\frac{1}{2T}\int_{-T}^{T}\abs{s(t)e^{ -2\pi xt}dt}^{2}\] (9)
* Power: \[\text{Power }(k)=\text{ }\int_{-\infty}^{\infty}\text{PSD}(x)\text{ }dx\] (10)
* Power Ratio: \[\text{Power Ratio }(x)=\frac{\text{Power}}{\text{Power Sum}}\] (11)where  
\[\text{Power Sum}=\sum_{k=1}^{5}\text{Power} \tag{12}\]  
The final category of features includes those derived from both the time and frequency domains. Although fewer in number, these features are frequently utilized in numerous studies [13; 64; 94; 103]. The principal time-frequency domain feature is the wavelet energy of the signals. Additionally, a feature known as wavelet entropy is notable in this domain. These two features can be characterized as follows:  
* Wavelet Energy: \[\text{ENG}(x)=\sum_{t=1}^{n}(x(t))^{2}\] (13)
* Wavelet Entropy: \[\text{ENT}(x)=-\sum_{t=1}^{n}(x(t))^{2}\log{(x(t))^{2}})\] (14)