## 2 Algorithms in the Classification System  
### Extraction Method of MFCC  
The core of MFCC is to simulate the characteristics of human beings' auditory perception to obtain a set of characteristic parameters of acoustic signals [38]. The sensitivity of the human auditory system is unstable and varies with frequency. MFCC attempts to simulate this kind of nonlinear characteristic of the human ear by converting the actual frequency into the mel frequency domain. The conversion relationship between mel frequency and actual frequency is as follows [39]:  
\[f_{mel}=2952\times lg\left(1+\frac{f}{700}\right), \tag{1}\]  
where \(f_{mel}\) represents the mel frequency and \(f\) is the actual frequency, as shown in Figure 1.  
MFCC features are extracted through the following steps: FFT transform, mel filtering, logarithmic transform, and discrete cosine transform (DCT) [38]. Mel filtering uses the filter bank composed of several triangle bandpass filters which are distributed evenly on the mel frequency domain to convert the signal to mel frequency and the filter bank [40] is  
\[H_{m}(k)=\left\{\begin{array}{cc}0,&f(k)\textless f(m-1)\text{ or }f(k)>f(m+1)\\ &\frac{2|k-f(m-1)|}{|f(m+1)-f(m-1)|/|f(m-1)|},\\ &f(m-1)\textless f(k)\leq f(m)\\ &\frac{2|f(m+1)-k|}{|f(m+1)-f(m-1)|/|f(m+1)-f(m)|},\\ &f(m)\leq f(k)\leq f(m+1)\end{array}\right. \tag{2}\]  
where \(f(m)\) is the center frequency of the \(m\)-th triangular filter, and \(M\) is the total number of triangular filters, then, calculate as Equation (3) to obtain \(M\) features where \(X\) (\(k\)) is the FFT of the signal and \(N\) is the FFT length.  
\[s(m)=\ln\left[\sum_{k=0}^{N-1}\left|X(k)\right|^{2}H_{m}(k)\right],\text{ }0 <m<M \tag{3}\]  
Finally, MFCC features are obtained through discrete cosine transform with \(c(i)\) representing the \(i\)-th MFCC feature.  
\[c(i)=\sqrt{\frac{2}{N}}\sum_{j=1}^{p}m_{j}\cos\left[(j-0.5)\frac{\pi i}{M} \right],\text{ }1\leq i,j\leq M \tag{4}\]  
Since the features extracted above are static MFCC features which cannot reflect the changing trends of the acoustic signal, the delta MFCC features which are composed of the first- and second-order differences of the static MFCC features are proposed to describe dynamic characteristics of the signal. The delta MFCC features are calculated as Equations (5) and (6). In order to obtain the delta MFCC features of the same length as the static MFCC features, the forward difference and the backward difference are used to complement the first frame and the last frame, respectively [40].  
\[\Delta_{n}=\left\{\begin{array}{cc}c_{n+1}-c_{n},&n\leq K\\ \frac{\sum_{k=1}^{K}\left(c_{n+k}-c_{n+k}\right)}{\sqrt{2\sum_{k=1}^{K}k^{2}}}, \text{ }K+1\leq n\leq N-K\\ c_{n}-c_{n-1},&n\geq N-K+1\end{array}\right. \tag{5}\]  
\[\Delta\Delta_{n}=\left\{\begin{array}{cc}\Delta_{n+1}-\Delta_{n},&n\leq K\\ \frac{\sum_{k=1}^{K}\left(\Delta_{n+k}-\Delta_{n-k}\right)}{\sqrt{2\sum_{k=1}^ {K}k^{2}}},\text{ }K+1\leq n\leq N-K\\ \Delta_{n}-\Delta_{n-1},&n\geq N-K+1\end{array}\right. \tag{6}\]  
Figure 1: Graph indicating the relationship between mel frequency and actual frequency directly.  
where, respectively, \(\Delta_{n},\Delta\Delta_{n}\) represent the first- and second-order differences of static MFCC features of the \(n\)-th frame and \(K\) is the difference coefficient, generally \(K=2\).