## 2 Materials and Methods
### Data Preprocessing
#### 2.3.3 Feature Extraction  
A comprehensive literature review was conducted to improve the feature extraction process. Important studies by [PERSON] [27] were examined in detail, and feature selection was made in light of these studies. Among the selected features from the cepstral domain are Mel-Frequency Cepstral Coefficients (MFCCs). Zero crossing ratio (ZCR) and root mean square (RMS) features from the time domain were also considered, but only the MFCC feature was used in this study. Example MFCC images of each class are shown in Figure 1. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Class** & **Min. Duration (s)** & **Max. Duration (s)** & **Avg. Duration (s)** \\ \hline Belly pain & 5.70 & 8.19 & 6.93 \\ Burping & 6.40 & 7.94 & 6.94 \\ Discomfort & 5.87 & 8.28 & 6.95 \\ Hungry & 6.52 & 7.06 & 6.91 \\ Tired & 5.77 & 8.54 & 6.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Duration for Donate a Cry. Figure 1: Mel spectrogram example for each class. The step-by-step process for computing MFCC is illustrated in the block diagram in Figure 2. The block diagram presented in Figure 2 is given to explain the general operation of the MFCC calculation process. 1. Pre-Emphasis: The initial speech signal \(x(n)\) is passed through a high-pass filter to enhance higher frequency components [28]: \[y(n)=x(n)-a\cdot x(n-1)\] (1) Here, \(y(n)\) represents the filtered signal, and the coefficient \(a\) typically ranges between 0.9 and 1.0. This step emphasizes the higher frequencies, increasing their energy for improved feature extraction [29]. 2. Frame Blocking: The speech signal is typically divided into overlapping frames, each lasting between 20 and 30 ms. Frames have a certain amount of overlap, and the frame length is usually greater than this overlap. Commonly used values for frame length and overlap are 256 and 100, respectively [29]. 3. Windowing: Windowing is applied to reduce signal discontinuities at frame edges. A smooth window function, such as the Hamming window, is used, which tapers to zero at its extremes. This approach maintains signal continuity between frames. The Hamming window is defined as Formula (2): \[Y(n)=X(n)\cdot W(n)\] (2) Here, \(W(n)\) is the window function [29]. 4. Fast Fourier Transform (FFT): FFT converts the time domain signal into the frequency domain, facilitating feature extraction while retaining all essential information. The magnitude spectrum is smoothed using triangular band-pass filters to simplify speech processing [30]. 5. Discrete Cosine Transform (DCT): DCT is applied to the outputs of the band-pass filters to compute the Mel-Frequency Cepstral Coefficients (MFCCs). The transformation from the frequency domain back to the time domain is given by Formula (3): \[C(n)=\sum E_{k}\cdot\cos\Bigl{(}n\cdot(k-0.5)\cdot\frac{\pi}{40}\Bigr{)}\] (3) Here, \(n\) ranges from 0 to \(N\), \(N\) represents the number of triangular band-pass filters, and \(L\) is the number of Mel-scale Cepstral Coefficients. The k value is the index of the band-pass filters and usually represents the number of frequency components. This value indicates the order of the band-pass filters used. These coefficients are widely used in speech recognition tasks [30]. In this study, certain parameters are used to extract Mel-Frequency Cepstral Coefficient (MFCC) features from audio signals. The sampling frequency (sample rate) is selected as 16,000 Hz. This selection is a common standard, especially in speech and general audio processing applications and provides a sufficient resolution representation of the sound. Figure 2: Block diagram of the MFCC computation. The number of MFCC coefficients is determined as 13. Generally, the first few MFCC coefficients represent the basic spectral features of the sound, while higher coefficients capture fine details. Using 13 coefficients is a balanced choice in terms of both preventing information loss and keeping the processing load at a reasonable level. In MFCC calculation, instead of coefficients that vary over time, it is preferred to take average values.