# Combined Data Augmentation on EANN to Identify Indoor Anomalous Sound Event
## 2 Materials and Methods
### Mel-Frequency Cepstral Coefficients  
Mel-Frequency Cepstral Coefficients (MFCCs) are a widely adopted feature in the field of speech recognition, and their origins can be traced to the perceptual mechanisms of the human auditory system. The human auditory system has a unique structure that enables it to automatically distinguish between the low-frequency and high-frequency components of audio signals, with the low-frequency components carrying critical identification features. Based on this biological observation, researchers have employed a Mel scale strategy. By applying denser filters in the lower frequency range and sparser filters in the higher frequency range, this strategy simulates the perceptual characteristics of the human ear. Compared with Bark or ERB scale, Mel scale not only considers human ears' perception of sound loudness, but also human ears' perception of sound pitch. It can better capture the global characteristics of sound and is more suitable for abnormal sound detection [32]. The relationship between Mel frequency and linear frequency can be approximated by the following equation:  
\[\text{Mel}(f)=2595\times\log\left(1+\frac{f}{700}\right) \tag{1}\]  
where \(f\) represents frequency in Hertz (Hz). This method allows researchers to extract essential information from spectrogram data and convert it into Mel-frequency spectrogram representation. Figure 2 below illustrates the MFCC feature extraction process, which primarily consists of preprocessing, Fast Fourier Transform (FFT), Mel filterbank, logarithmic operation, and Discrete Cosine Transform (DCT). * represents the audio signal processed in the previous step.  
The preprocessing stage includes pre-emphasis, framing, and windowing. Pre-emphasis enhances the spectral content of the high-frequency part of the signal, making the spectral characteristics smoother. Framing divides the signal into several short-term segments, where each segment can be considered a stationary process. During framing, a common practice is to use half of the overlap frame length to split the signal, ensuring a smooth transition between frames. Windowing is applied to reduce signal truncation effects. After preprocessing, all frames undergo FFT processing, resulting in the discrete spectrum \(S(k)\) of the signal, as shown in Equation (2):  
\[S(k)=\sum_{n=0}^{N-1}s_{w}(n)exp^{-\frac{2\pi k}{N}},\ 0\leq k\leq N \tag{2}\]  
Figure 2: MFCC feature extraction process.  
where \(s_{w}(n)\) represents the sound signal after windowing, and \(N\) denotes the number of points for the Fourier Transform. Subsequently, the energy spectrum is filtered using \(M\) sets of triangular bandpass filters to obtain the Mel spectrogram. The logarithmic values of the Mel spectrogram are then applied to the inverse spectral transform, which converts a multiplicative signal into an additive one. This transformation emphasizes the low-frequency envelope characteristics and high-frequency detail features. In the cepstral analysis process, the DCT is employed to compute \(M\)-order logarithmic energies, resulting in \(L\)-order MFCC coefficients. The formula for DCT is represented as (3), where \(S_{m}^{*}\) represents the logarithmic energy spectrum, \(M\) is the number of triangular filters, and \(L\) denotes the order of MFCC coefficients (\(L\) = 12-16)  
\[C_{n}=\sum_{m=0}^{N-1}S_{m}^{*}\cos\frac{n\pi(m-0.5)}{M},n=1,2,\cdots,L. \tag{3}\]  
The MFCC spectrograms of several types of abnormal sound events studied in this paper are illustrated in Figure 3, as shown below. The different colors represent the energy distribution.