# DIFFBAS: An Advanced Binaural Audio Synthesis Model Focusing on Binaural Differences Recovery
## 3 Experiments and Results
### Experiment Results
#### 3.2.2 Quantitative Evaluation  
Comparative experimentWe compared the quality of binaural audio synthesized by the following systems:  
* **Geo-Warp**, which performs time translation and amplitude alteration on the left and right ear signals based on the geometric information and attenuation formula of the distance from the sound source to both ears. * **WarpNet**, which transforms the time-domain waveform to obtain binaural audio through geometric warp and neural warp. * **NFS**, which generates frequency domain masks based on position information to obtain binaural audio. * **DIFFBAS + WarpNet**, the backbone network of DIFFBAS is WarpNet. * **DIFFBAS + NFS**, the backbone network of DIFFBAS is NFS. To demonstrate the deficiency of previously used metrics, we add two dummy BAS systems for comparison:  
* **Mono-Mono**, which produces binaural audio simply by copying the mono audio of the sound source to the left and right channels. * **Avg-Avg**, which produces binaural audio by copying the average signals of left and right channels. The results of the comparative experiments are summarized in Table 4.  
It can be seen that DNN-based methods are better than Geo-Warp, which shows that rough time translation and amplitude alteration based only on geometric information cannot model accurate and real binaural audio, and can only retain fuzzy spatial information. In terms of binaural difference recovery, compared with WarpNet, the IPD error of DIFFBAS + WarpNet is greatly reduced from 1.064 to 0.834. Similarly, the IPD error of DIFFBAS + NFS is also reduced from 1.250 to 1.083. Therefore, DIFFBAS can significantly improve the accuracy of the synthesized audio referring to its interaural phase  
Figure 5: Development of phase error (\(\mathcal{L}_{\text{pls}}\)) and interaural phase difference error (\(\mathcal{L}_{\text{IPD}}\)) as the \(\mathcal{L}_{2}\)-loss decreases during training on WarpNet [15] using different loss functions. The blue line represents the changing trend of \(\mathcal{L}_{\text{pls}}\), and the orange line represents the trend of \(\mathcal{L}_{\text{IPD}}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\mathbf{\mathcal{L}_{2}\times 10^{3}\downarrow}\) & \(\mathbf{Amp\downarrow}\) & \(\mathcal{L}_{\text{pls}}\downarrow\) & \(\mathcal{L}_{\text{IPD}}\downarrow\) \\ \hline power spectrum+phase copy [25] & 1.276 & 0.048 & 1.563 & - \\ multiscale STFT [15] & 2.279 & 0.043 & 1.996 & - \\ Si-SDR [28] & 0.798 & 0.222 & 1.507 & - \\ \(\mathcal{L}_{2}\) & 0.146 & **0.033** & 0.894 & 1.217 \\ \(\mathcal{L}_{2}+\mathcal{L}_{\text{pls}}\) & 0.145 & 0.036 & **0.815** & 1.064 \\ \(\mathcal{L}_{2}+\mathcal{L}_{\text{pls}}+\mathcal{L}_{\text{IPD}}\) (Equation (14)) & **0.142** & 0.036 & 0.819 & **0.967** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of commonly used losses for audio modeling to our proposed loss. The \(\downarrow\) symbol indicates that the lower the metric, the better the effect. The optimal value of each metric is shown in bold. differences. At the same time, the losses of other metrics are also reduced, which means that the introduction of IPD loss will not impact the supervision of other losses. In addition, the human auditory system is most sensitive to the phase difference information of low-frequency signals, especially for the high-energy parts. Therefore, we randomly selected a 2-second audio segment and performed STFT, screened out the low-frequency parts, and calculated the frequencies with peak energy at different time points. We compute the IPD of synthesized audio at the frequency with the peak energy at each time. Then, the IPD values of synthesized audio are compared with the IPD values of the ground truth audio, the results of which have been shown in Figure 6. It can be seen that DIFFBAS can synthesize binaural audio whose IPD is almost consistent with the ground truth at the frequency with the highest energy. In addition, Figure 7 shows the IPD error heatmaps at different frequencies for the same four models as above during the same time period.