## 2 Introduction of Speech Feature Representation and Acoustic Model Configuration
### Mel-Frequency Cepstral Coefficients and Mel-Frequency Filter-Bank Features  
Mel-frequency filter-bank features (FBANK) and mel-frequency cepstral coefficients (MFCC) are two of the most widely used speech feature representations in the state-of-the-art ASR system. FBANK and MFCC approximate the response of the human auditory system to sounds better than the linearly scaled frequency-band energies (short-time Fourier transforms of sound segments), thereby corresponding to superior recognition accuracies in ASR. The procedures of creating a series of FBANK and MFCC features from an utterance are depicted in Figure 1. From this figure, it is clear that computing FBANK is the same as computing MFCC except for the discrete cosine transform (DCT) in the final step. The DCT operation is believed to reduce the correlation of the input significantly, and thus MFCC features are much less correlated than FBANK features. It is noteworthy that in conventional ASR systems, MFCC is preferred over FBANK due to its nearly uncorrelated characteristic. However, FBANK usually behaves better than MFCC in some advanced ASR systems whose acoustic models are non-sensitive to feature correlation. In the following, we briefly introduce each MFCC/FBANK creation procedure shown in Figure 1.  
1. _Pre-emphasis:_ The first step is to apply a pre-emphasis filter on the input signal to amplify the high-frequency components because utterances usually have smaller magnitudes in high frequencies compared to low frequencies. The pre-emphasis filter can be applied to a signal \(x[n]\) as the following equation: \[y[n]=x[n]-0.97x[n-1].\] (1)2. _Framing:_ An utterance is non-stationary, and its inherent characteristics change over time. However, it is reasonable to assume that the characteristics remain unchanged in each short-time interval. Thus, the utterance is segmented into a series of partially overlapped frames. The frame duration and frame shift are usually set to 25 ms and 10 ms, respectively. 3. _Windowing:_ After framing, each frame signal is multiplied with an appropriate window function to reduce the unwanted sidelobes in spectrum [29]. We usually use the Hamming window function here, which is: \[w[n]=0.53836-0.46164\cos(\frac{2\pi n}{N-1}),n=0,1,\ldots,N-1,\] (2) where \(N\) is the frame size. 4. _Discrete Fourier transform (DFT):_ The windowed time-domain frame signal is converted to the acoustic frequency domain via a discrete Fourier transform (DFT). In the frequency domain, the signal's human hearing characteristics (such as formants and pitches) can be better revealed. The function of the DFT is as follows: \[X[k]=\sum_{n=0}^{N-1}x[n]e^{-j\frac{2\pi n}{N}},k=0,1,\ldots,N-1.\] (3)
5. _Mel-frequency wrapping:_ The perceived frequency resolution in the human hearing mechanism decreases as the physical frequencies increase, making humans less sensitive to frequency change at high frequencies. The mel-filter-banks, which consist of triangular band-pass filters, are designed to simulate the above mechanism by locating more narrow-bandwidth filters at low frequencies and fewer wide-bandwidth filters at high frequencies. The \(l\)th mel-filter \(H_{l}[k]\) of the filter-bank is defined by: \[H_{l}[k]=\left\{ \begin{array}{cc}0,&k<f[l-1]\\ \frac{k-f[l-1]}{f[l-1]},&f[l-1]\leq k\leq f[l]\\ \frac{f[l-1]-k}{f[l-1]-f[l]},&f[l]\leq k\leq f[l+1]\\ 0,&k>f[l+1]\end{array} \right.\] (4) in which \(f[l]\) denotes the center frequency of the \(l\)th mel-filter, calculated by: \[f[l]=\frac{N}{f_{s}}mel^{-1}[mel(f_{l})+l\frac{mel(f_{H})-mel(f_{L})}{J+1}]\] (5) with \(f_{H}\) and \(f_{L}\) being, respectively, the highest and lowest frequencies and \[mel(f)=2595\log_{10}(1+\frac{f}{700})\] (6) which transforms the acoustic frequency \(f\) (in Hz) to the perceptual frequency \(mel\). With the set of mel-filters, we convert the magnitude spectrum \(|X[k]|\) for each frame to the mel-scaled (magnitude) spectrum: \[S[l]=\sum_{k=0}^{\frac{N}{2}-1}H_{l}[k]|X[k]|,l=1,2,\ldots,L\] (7)
6.