## 3 Methodology
### Feature Extraction and Selection
#### 3.2.11 Statistical Features  
Mean  
This is the signal's average amplitude over a considered time interval. This feature is considered because the mean value of abnormal PCGs vs. normal PCGs is higher. It is defined by\[\mu=\frac{1}{N}\sum_{i=0}^{N-1}x_{i} \tag{14}\]  
where \(x_{i}\) represents ith amplitude instance in the signal, and N is the total number of instances. Mode  
The mode is a fundamental measure of central tendency that identifies the value or values that occur most frequently within a dataset. Unlike the mean and median, which provide a numerical average or a central value, respectively, the mode offers insights into the most common or repetitive patterns in the data. There are a few key characteristics of the mode:  
* It directly reflects the highest peak of the data distribution, indicating where data samples are most densely concentrated. * A dataset can have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode at all. * The mode is particularly robust against outliers or extreme values. Since it is based solely on the frequency of occurrence, it remains unaffected by the magnitude of data points, making it a reliable measure in datasets with potential anomalies. In the context of signal analysis, the mode becomes especially pertinent. Given that signals often contain repetitive patterns or recurring values, identifying the mode can provide insights into the inherent characteristics or the \"essence\" of the signal. For instance, in medical signal analysis, the mode can help differentiate between normal and abnormal signals by highlighting the most common patterns present. If a particular value or pattern frequently appears in a normal signal but is absent or less frequent in an abnormal one, the mode can be a distinguishing feature. By incorporating the mode as a feature in the analysis, this work aimed to harness its resilience against extreme values and its ability to capture the core patterns of the signal. This ensures a more accurate and reliable differentiation between different classes or categories of signals, enhancing the overall efficacy of the analysis. Median  
The median is a central measure of tendency that provides significant insights into the distribution of a dataset. Unlike the mean, which takes into account all values in a dataset, the median focuses solely on the middle value, making it resistant to outliers or extreme values. This characteristic ensures that the median provides a more robust representation of the central location of data, especially in skewed distributions. In a dataset arranged in non-decreasing order, we have the following:  
* If the number of observations, denoted as \(n\), is odd, then the median is the value at the exact middle position, which can be mathematically represented as the value at the \((n+1)/2\)th position. * If \(n\) is even, the median is typically calculated as the average of the two middle values, specifically the values at the \(n/2\)th and \((n/2)+1\)th positions. By this definition, exactly 50.00% of the observations in the dataset lie below the median, and the remaining 50.00% lie above it. This property makes the median a particularly valuable metric in understanding the central tendency of a dataset, as it divides the dataset into two equal halves in terms of the number of observations, regardless of the actual values of those observations. Given its resistance to extreme values, the median is often preferred over the mean in datasets that may contain outliers or when the distribution of data is notably skewed. It clarifies \"typical\" values in such scenarios, ensuring that a few extreme observations do not unduly influence the central tendency. This is an important statistical feature that helps determine how much the sample under process deviates from its mean value. A higher standard deviation indicates that the data are spread over a wider range, whereas a lower deviation means the data points are closer to the mean. This helps differentiate between normal and abnormal PCGs.