## 2 Materials and Methods
### The Proposed Model
#### 2.2.2 Mel-Scale Spectrogram  
The perception of sound by the human ear is highly complex and nonlinear, particularly across different frequency ranges where distinct perceptual differences arise. However, insect sound signals often span a wide frequency range. In addition, human ear perception differs from a linear frequency scale. As frequency increases, human auditory sensitivity decreases, resulting in much smaller perceptual differences for high-frequency sounds compared to low-frequency sounds. To better simulate the auditory behavior of the human ear,  
Figure 2: Overall flow of the proposed deep learning model for insect sound classification.  
we propose using the Mel scale [33], a nonlinear frequency scale. It converts the ordinary frequency (Hertz) f into the Mel frequency (Mel) m using Equation (1):  
\[M(f)=2595\cdot lg(1+\frac{f}{700}) \tag{1}\]  
To map spectral information to the Mel-scale frequency domain, we utilize a set of Mel filters [34]. These filters are evenly distributed on the Mel scale. The center frequencies of these Mel filters are configured according to the Mel scale to mimic the way the human ear perceives sound.  
Creating the Mel spectrum entails convolving the spectral data obtained through the short-time fourier transform (STFT) [35] with the response of each Mel filter and computing the energy \(E_{i}\) within each frequency band of the Mel filter. This step generates an energy value for each frequency band using Equation (2), resulting in the formation of the Mel spectrum. The STFT, on the other hand, transforms audio data from the time domain to the frequency domain. It decomposes the signal into frequency components within a series of time windows and conducts the transformation of audio data and spectral information as per Equation (3). Here, \(X(t,f)\) represents the complex representation at time \(t\) and frequency \(f\), \(x(\tau)\) stands for the input audio signal, \(\omega(\tau-t)\) corresponds to the window function, and \(e^{-j2\pi ft}\) denotes the complex exponential term. Spectrograms, or Mel spectrograms, portray the signal's strength over time at different frequencies by using a variety of colors for visual representation.  
\[E_{i}=\sum_{f}|X(t,f)|^{2} \tag{2}\]  
\[X(t,f)=\int_{-\infty}^{\infty}x(\tau)\cdot\omega(\tau-t)\cdot e^{-j2\pi ft}d\tau \tag{3}\]  
By applying a logarithmic transformation to the Mel spectrogram, we enhance the features and map them to a range more suitable for deep learning models, resulting in the logarithmic Mel spectrogram. This captures the fundamental characteristics of the audio. Building upon this, we apply the SpecAugment technique [36] to the logarithmic Mel spectrogram, as shown in Figure 4. Introducing horizontal bars via frequency masking and randomly masking time ranges by blocking vertical lines in the spectrogram. This is used to increase data diversity, simulate noise in different environments, or adjust the spectral characteristics of the signal, further enhancing data augmentation.  
Figure 3: Data Augmentation Diagram ((**a**): Original Image, (**b**): Noise Addition, (**c**): Pitch Shifting, (**d**): Time Stretching, (**e**): Time Shifting).