# Quality Enhancement of MPEG-H 3 DA Binaural Rendering Using a Spectral Compensation Technique
## 4 Implementation and Complexity
\[SD(b)=20\log_{10}\sqrt{\frac{1}{2\cdot N_{b}}\sum_{j=L,R}\sum_{k\in K_{b}}\left(| \hat{H}^{j}_{BR}(k)|-|H^{j}_{ref}(k)|\right)^{2}}, \tag{16}\]  
where \(K_{b}\) is a set of FFT bins belonging to the \(b\)th band and \(N_{b}\) is the number of bins in the set \(K_{b}\). The ILD error is measured as a difference between ILDs for the true and compensated HRTF cases using a definition of ILD: \(ILD(b)=10\log_{10}(\sum_{k\in K_{b}}|H^{L}(k)|^{2}/\sum_{k\in K_{b}}|H^{R}(k)|^ {2})\), where \(H_{L}(k)\) and \(H^{R}(k)\) are the left and right ear HRTFs, respectively. Since there is no trend difference for the different HRTF dataset in all experiments, the SD and ILD error are averaged for all HRTF dataset. Table 3 shows the SD measured in an octave band scale of MPEG-H 3 DA BR, and MPEG-H 3 DA BR with the PGC and BSC, respectively. The frequency band marked with an asterisk indicates that the confidence intervals between the PGC and BSC do not overlap. The SD improvement of the PGC is 0.2-0.5 dB higher than that of the BSC in the 1.5-12 kHz frequency band, since the compensation gain of the BSC is limited. For the same reason, the standard deviation of the PGC is also smaller than that of the BSC in the 0.75-6 kHz frequency band. Thus, it is verified that the PGC compensates spectral artifacts more effectively than the BSC. Note that there is no difference in an octave band ILD error between the two methods. The SD and ILD errors of the MPEG-H 3 DA BR with and without the proposed algorithm described in Section 4 are shown in Figure 6a,b. In Figure 6a, the proposed algorithm improves SD by about 2.5 dB below 750 Hz. This low-frequency range is where spectral boosts often occur since the phase difference between HRTFs is negligible. In the frequency range from 3 kHz to 12 kHz, where the spectral notch and boost simultaneously occur, the SD improvement decreases to 0.8\(\sim\)2 dB on average. The trend slightly changes as the frequency increases; however, the proposed method clearly reduces SD in all frequency bands. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Freq. Range** & **0-0.75 kHz \({}^{*}\)** & **0.75-1.5 kHz \({}^{*}\)** & **1.5-3 kHz \({}^{*}\)** & **3-6 kHz \({}^{*}\)** & **6-12 kHz \({}^{*}\)** & **12-18 kHz** \\ \hline MPEG-H 3 DA BR & 2.91 (\(\pm\)0.95) dB & 2.47 (\(\pm\)1.27) dB & 2.95 (\(\pm\)2.34) dB & 3.90 (\(\pm\)2.66) dB & 4.77 (\(\pm\)2.28) dB & 5.57 (\(\pm\)2.52) dB \\ \hline MPEG-H 3 DA BR & 0.44 (\(\pm\)0.25) dB & 0.90 (\(\pm\)0.71) dB & 1.84 (\(\pm\)1.70) dB & 2.40 (\(\pm\)1.93) dB & 3.91 (\(\pm\)2.01) dB & 4.85 (\(\pm\)2.32) dB \\ \hline MPEG-H 3 DA BR & 0.46 (\(\pm\)0.26) dB & 0.86 (\(\pm\)0.58) dB & 1.62 (\(\pm\)1.30) dB & 1.87 (\(\pm\)1.17) dB & 3.72 (\(\pm\)1.96) dB & 4.79 (\(\pm\)2.36) dB \\ \hline \hline \end{tabular}  
* Frequency band where the confidence intervals between the PGC and BSC do not overlap.  
\end{table} 
Table 3: Mean and standard deviation of the SD measurement of MPEG-H 3 DA BR, and MPEG-H 3 DA BR with PGC and BSC, respectively. Figure 6: Measurement results of (**a**) SD and (**b**) ILD error with a 95% confidence interval, measured in octave bands. In Figure 6b, the proposed algorithm maintains the ILD error within 0.5 dB in all octave bands. This means that after applying the proposed algorithm, the perceptual error becomes negligible, as it is below the just noticeable difference (JND) [19]. Based on these improvements, we argue that the compensation scheme of the proposed algorithm successfully reduces the spectral artifacts by the comb filter effect while preserving the localization of the original rendering.