## 3 Methods
### Feature Extraction
#### 3.2.5. Morphological Features  
Extracting morphological features from ECG and GSR signals facilitates a detailed evaluation of their structural characteristics. The key morphological features derived from these signals include their width, area, skewness, kurtosis, and slope. Width: In the context of signal analysis, 'width' refers to the time span of a distinct segment of the signal. This metric is essential for understanding the timing and persistence of physiological processes. Analysis of the width of ECG and GSR signals enables the identification of temporal patterns and events within the physiological data, thus aiding in the differentiation of typical and atypical physiological responses. To calculate the width, the onset and conclusion of the relevant signal fragment are pinpointed, with the width being the interval between these two temporal markers. \[\text{Width}=t_{\text{end}}-t_{\text{start}} \tag{3}\]  
where \(t_{\text{end}}\) is the ending time and \(t_{\text{start}}\) is the starting time of the signal component of interest [41]. Figure 4: Sample GSR series illustrating the physiological responses associated with the five emotions defined in this study. Area: The area feature is determined by computing the integral of the absolute value of the signal over a specified time interval. This metric offers a quantification of the total activity or magnitude of the signal within that interval. Analyzing the area under the curve for ECG and GSR signals allows researchers to gauge the cumulative magnitude of physiological responses. Variations in the area metric can reflect changes in the intensity or overall magnitude of physiological activities. \[\text{Area}=\int|x(t)|\,dt \tag{4}\]  
where \(x(t)\) represents the signal, and the integral is evaluated over the specified time interval of interest [42]. Skewness: Skewness is a statistical metric that evaluates the asymmetry in the distribution of signal amplitude values. This measure sheds light on the signal's distribution, indicating whether it leans more towards positive or negative values. Analyzing the skewness of ECG and GSR signals allows for the identification of the dominant trend in the amplitude distributions, which is instrumental in delineating specific physiological response patterns. The skewness is determined by employing the following formula:  
\[\text{Skewness}=E\bigg{[}\bigg{(}\frac{x(t)-\mu}{\sigma}\bigg{)}^{3}\bigg{]} \tag{5}\]  
where \(E\) denotes the expected value, \(x(t)\) represents the signal, \(\mu\) is the mean of the signal, and \(\sigma\) is the standard deviation of the signal. The term \(\bigg{(}\frac{x(t)-\mu}{\sigma}\bigg{)}^{3}\) is cubed to normalize the skewness measure, ensuring it is dimensionless and provides a consistent scale for comparison [43]. Kurtosis: In signal analysis, kurtosis is a statistical metric that quantifies the distribution's \"peakedness\" or its deviation from being flat-topped. This measure is instrumental in detecting outliers or extreme values within a dataset. When applied to ECG and GSR signals, kurtosis analysis sheds light on the form and distribution tendencies of the signal amplitudes. Any departure from typical kurtosis values could signal unusual physiological reactions or anomalies within the signal. The computation of kurtosis is facilitated through the following formula:  
\[\text{Kurtosis}=E\bigg{[}\bigg{(}\frac{x(t)-\mu}{\sigma}\bigg{)}^{4}\bigg{]}-3 \tag{6}\]  
In this expression, \(x(t)\) denotes the signal at time \(t\), \(\mu\) is the mean of the signal, \(\sigma\) represents the standard deviation of the signal, and \(E[\cdot]\) signifies the expected value. The subtraction of 3 adjusts the kurtosis value to zero for a normal distribution [44]. The term \(\bigg{(}\frac{x(t)-\mu}{\sigma}\bigg{)}^{4}\) is raised to the fourth power to normalize the kurtosis measure. The addition of \"\(-3\)\" at the end of the formula results in _excess kurtosis_, which is used to compare the kurtosis of the given distribution with that of a normal distribution.