# A Deep Neural Network Model for Speaker Identification
## 2 Materials and Methods
### Experimental Setup
#### 2.3.2 Data Preprocessing  
In data preprocessing, our goal is to obtain the spectrogram, which contains rich acoustic features of speakers. The spectrogram is obtained by framing, windowing, short-time Fourier transform (STFT) [45], etc. The STFT is a process that computing the discrete Fourier transforms (DFT) of a signal over short overlapping windows. Short overlapping windows can maintain the short-time stability of speech signals in speech signal processing. The sampling frequency of the speech was 16 kHz, and the number of FFT points in this experiment was 512. The discrete STFT of the framed speech signal is calculated by the following equation:  
\[X[k]=\sum_{n=0}^{N-1}x[n]e^{-j\frac{2\pi nk}{N}}\quad k=0,1,2,...,N-1. \tag{17}\]  
Here, \(x[n]\) denotes the framed signal with \(n\) as the sequence number in the frame, \(N\) denotes the frame size. The power spectrum is defined by using Formula (18):  
\[P(k)=|X(k)|^{2}. \tag{18}\]  
In our experiment, after loading an audio file, a floating-point time series was obtained. After its energy spectrum was calculated, then it was converted onto the Mel scale [53]. Additionally, more analysis can be extended after converting a power spectrum (amplitude squared) to decibel units. In this process, the frame length was set to 32 milliseconds, the window shift between successive frames is 16 milliseconds, and the window function selects the Hamming window. Finally, we got the spectrogram as shown in Figure 6, and the specific process of preprocessing is shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Speakers** & **Utterances** & **Ratio** \\ \hline Training data & 400 & 127,551 & 90\% \\ Validation data & 400 & 7278 & 5\% \\ Test data & 400 & 7096 & 5\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: The usage of the Aishell-1 dataset in experiments.  
The spectrogram combines the advantages of the time domain and frequency domain. At the same time, it obviously contains the change of speech spectrum along with time. As shown in Figure 6, the x-axis of the spectrogram is time, the y-axis is frequency, and the brightness represents amplitude: Darker, smaller; brighter, larger. The energy distribution of different frequency signals can be seen in the spectrogram. Additionally, the intensity of any given frequency component at a given time is expressed by color depth. Different degrees of black and white on the spectrogram form different lines, which are called voiceprint [7].  
Finally, we compute delta features from the vector sequence, which is to calculate the feature vectors based on preceding and following N frames, the result is called the first-order features and the second-order features when N is 1 and 2.  
In our study, the first-order features and second-order features are combined with the log Mel-filterbank energy features into a numpy [54] array. After performing some mathematical processing on feature vectors, a multidimensional tensor is sent into the convolutional layer for feature extraction. Then, the model is trained through iterative computations.  
Figure 6: Spectrogram of speech. The intensity of any given frequency component at a given time is expressed by color depth. Darker, smaller; brighter, larger.  
Figure 7: The process of the data preprocessing. The purpose of the preprocessing process is to obtain a spectrogram of the speech signal for further analysis.