## 4 Evaluation
### Objective Evaluation Results According to the PD Weights and the Length of the HE Filter  
The various results were obtained by changing the weight for the PD term in (12), \(w_{s}\), while the weight for the MSE was given by \(w_{M}=1-w_{s}\). We also investigated how the objective performance was affected according to the length of the HE filter coefficients. Note that assigning zero to the weight of the PD term corresponds to the conventional MSE-based prediction rules. In a similar manner, a zero length for the HE filter meant that HE was not adopted in the SSI system, and, hence, the source signals were generated by white noise. The results are presented in Figure 6 where \(N_{k}\) denotes the length of the HE filter coefficients. A strong correlation (0.9551) between the average PESQ and \(N_{k}\) was observed in the case of \(w_{s}=0\). This means that the perceptual quality can be improved by applying HE even when the perceptual distance is not adopted. The PESQs were further increased by including the perceptual distance into the DNN loss function. In the case of \(w_{s}=0.25\), maximum PESQs were obtained for all \(N_{k}\). The average PESQ is also proportional to the length of the HE filter coefficients in this case (\(\rho=0.8109\)). And hence, the highest PESQ  
Figure 5: Objective evaluation results according to the weights of the asymmetrical disturbance. (**Top**): Average PESQs. (**Middle**): STOIs. (**Bottom**): LSDs. of 2.108 was achieved when \(N_{k}\) and \(w_{s}\) were set as 5 and 0.25, respectively. This was 0.11 higher than in the case of no HE. No further increase was observed when a weight greater than 0.5 was applied. This trend was common for HE filters of all lengths. When the relative weight for the PD term exceeded 0.5, the weight for the MSE term was less than 0.5. This resulted in excessive differences between the predicted spectra and the actual spectra, even though the resultant predicted spectra perceptually approximated the actual spectra. The testing of significance (two-way ANOVA) showed that the weight value was a major factor affecting the PESQ (\(p\) = 1.7 \(\times\) 10\({}^{-5}\)) and an average Pearson correlation coefficient of 0.8191 was obtained between the PESQs and the weight values. That result indicated that the performance in terms of PESQ was remarkably improved by employing the PD in the objective function. However, excessive emphasis on the PD term in the objective function actually degraded the PESQ, as shown in the PESQ values for \(w_{s}>0.5\). This means that improvements in PESQ can be accomplished by not only considering the MSE but the PD as well. Figure 6: Objective evaluation results for the various perceptual distance weights and the taps of the HE filters (\(N_{k}\)). (**Top**): Average PESQs. (**Middle**): STOIs. (**Bottom**): LSDs. There was a clear relationship between the STOIs and the perceptual weights, as shown in the middle of Figure 6. The average STOI values take the form of decreasing curves with increases in the weights of the perceptual distance. Unlike the PESQ, the STOIs are not remarkably changed by the length of the HE filter coefficients (\(p=0.2302\), \(\rho=0.4060\)). The average STOIs were significantly varied according to the PD weight. The \(p\)-value of the \(w_{s}\) factor was 4.61 \(\times\) 10\({}^{-10}\) and the Pearson correlation coefficient of the STOI with the \(w_{s}\) was \(-0.8930\). This indicated that the weight for the PD was the key factor affecting STOI. It is noteworthy that the maximum STOIs among all perceptual distance weights are obtained at \(w_{s}=0.25\), which is same as in the case of the PESQ. The average correlation between the LSD and the value of the PD weight was 0.8365. This indicates that the LSD takes the form of increasing curves with increases in the PD weight. This result was somewhat expected, because LSD is closely related to MSE. Increasing the weight of the PD means lowering the MSE weight, which results in a larger spectral distortion.