# A Multi-Frame PCA-Based Stereo Audio Coding Method
## 4 PCA-Based Parametric Stereo
### Subbands and Bitrate  
The spectrums of signal are divided into several segments based on Equivalent Rectangular Bands (ERB) model. The subbands are shown in Table 4.  
The quantization of space parameters uses ordinary vector quantization. The codebook with different parameters is designed based on the sensitivity of the human ear and the range of the parameter fluctuation of the experimental corpus. The codebooks of ILD and IC are shown in Tables 5 and 6, respectively.  
According to the above codebooks, the ILD parameters of each subband are quantized using 4 bits, and the IC parameters of each subband are quantized using 3 bits. According to the above sub-band division, the number of sub-bands higher than 1.6 kHz accounts for half of the total number of sub-bands in the whole frequency domain, which is 13, so the number of bits needed for each frame's spatial parameter is 13 \(\times\) 7 = 91. For frequencies above 1.6 kHz, the rate of quantitative parameters is about 4.5 kbps. In the frequency domain less than 1.6 kHz, the first principal component is used to describe the signal directly. The rate of transmission of the first principal component is around 10 kbps, so the parameter rate of PCA-based parametric stereo is around 15 kbps. In traditional parametric stereo [24], IPD of each subband is quantized by 3 bits, so the parameter rate of the traditional parameter stereo is about (4 + 3 + 3 + 3) \(\times\) 25 \(\times\) 50 = 16.25 kbps. Therefore, compared with traditional parametric stereo, the rate of PCA-based parametric stereo is slightly reduced.  
Figure 16 shows the results of a 0-1 test for spatial sense. In this test, 12 stereo music from EBU test materials is chosen. Score 0 means the sound localization is stable, and score 1 means there are some unstable sound localization in test materials. The ratio in Figure 16 is calculated from the times of unstable localization, and lower ratio means better performance in the quality of spatial sense. Experiments show that compared with the traditional parametric stereo encoding method, the spatial sense of the audio source has been obviously improved through the PCA-based parametric stereo. Through the use of PCA, almost half of the amount of parameter estimation can be reduced, while the computational complexity still rises because of the increasing complexity of PCA.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**index** & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
**IC** & 1 & 0.94 & 0.84 & 0.6 & 0.36 & 0 & \(-\)0.56 & \(-\)1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Codebook for IC. (IC, Interaural Coherence).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**index** & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
**start** & 0 & 100 & 200 & 300 & 400 & 510 & 630 & 760 \\ \hline
**index** & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
**start** & 900 & 1040 & 1200 & 1380 & 1600 & 1860 & 2160 & 2560 \\ \hline
**index** & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 \\
**start** & 3040 & 3680 & 4400 & 5300 & 6400 & 7700 & 9500 & 12,000 \\ \hline
**index** & 24 & 25 & & & & & & \\
**start** & 15,500 & 19,880 & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Subband division.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**index** & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
**IC** & 1 & 0.94 & 0.84 & 0.6 & 0.36 & 0 & \(-\)0.56 & \(-\)1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Codebook for ILD. (ILD, Interaural Level Difference).