# Auralization of High-Order Directional Sources from First-Order RIR Measurements
## 3 Listening Experiment--Comparative Study
### Results and Discussion
The \(Em\)-based auralization was the least consistent and produced the smallest lateralisation for \(\varphi_{S}=-82^{\circ}\) and \(\varphi_{S}=90^{\circ}\) compared to the other techniques. This is particularly pronounced for \(\varphi_{S}=90^{\circ}\) where there is more direct sound. _Distance:_ The median values and 95% confidence intervals for all beam directions and auralization techniques are shown in Figure 10 and the in \(p\)-values between the reference condition (\(Dy\)) and the other techniques are presented in Table 2. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \(\varphi_{S}=0^{\circ}\) & \(\varphi_{S}=-36^{\circ}\) & \(\varphi_{S}=-82^{\circ}\) & \(\varphi_{S}=180^{\circ}\) & \(\varphi_{S}=90^{\circ}\) \\ \hline  & & & \multicolumn{2}{c}{\(Dy\)} & \\ \hline \(Em\) & 0.00 & **0.15** & **1.38** & **0.70** & 0.00 \\ \hline \(As\) & 0.00 & **0.08** & **1.77** & **0.17** & **0.52** \\ \hline \(Sr\) & **0.76** & **0.23** & **3.76** & **0.07** & **0.07** \\ \hline \(Si\) & **0.30** & **0.15** & **3.76** & 0.00 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(p\)-values (Wilcoxon signed-rank test with Bonferroni-Holm correction) for ratings of direction. Insignificant differences (\(p\)-values \(\geq 0.05\)) are indicated by bold numbers. Figure 9: Median value and 95% confidence interval of direction ratings per beam direction \(\varphi_{S}\). Please note the varying \(y\)-axis as per sub-figure a range of \([15^{\circ},-25^{\circ}]\) around the median of the \(Dy\) ratings is shown. We found that the congruence of the distance mapping is high for all tested auralization techniques, almost independently of the specific beam directions \(\varphi_{S}\). The only exception is the \(Em\) based auralization, where for \(\varphi_{S}=180^{\circ}\) the source is perceived significantly further away. Discussion:The five different auralization techniques used to virtualize the IKO all involve measurements of RIRs. The results from the presented listening experiment verify that all tested techniques are able to qualitatively reproduce the perceptual effects known from studies involving the physical IKO [5, 7], cf. ellipses in Figure 7. Moreover, still, a detailed analysis of the perceptual attributes of direction, and distance, indicates some significant differences to the reference condition (dummy head based rendering \(Dy\)) for specific combinations of technique and beam direction, with some noticeable trend. In order to give an indication of the directional mapping quality of all tested auralization techniques, the mean direction offset to the \(Dy\) technique is listed in Table 3. Overall, the \(Em\) techniques yields with \(5.72^{\circ}\) the largest incongru fluence in directional mapping, while the errors of \(As\), \(Sr\), and \(Si\) roughly stay below \(2^{\circ}\). The mean distance offset between \(Dy\) and all other techniques pooled for all beam directions \(\varphi_{S}\) is given in Table 4. With a mean distance error of \(0.28\)m the \(As\), and \(Sr\) auralizations clearly outperform the \(Em\), and \(Si\) techniques. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(\varphi_{S}=0^{\circ}\) & \(\varphi_{S}=-36^{\circ}\) & \(\varphi_{S}=-82^{\circ}\) & \(\varphi_{S}=180^{\circ}\) & \(\varphi_{S}=90^{\circ}\) \\ \hline \multicolumn{7}{c}{\(Dy\)} \\ \hline \(Em\) & **1.14** & **0.78** & **0.49** & 0.02 & **1.27** \\ \hline \(As\) & **3.40** & **0.78** & **0.91** & **1.52** & **0.47** \\ \hline \(Sr\) & **3.24** & **0.65** & **2.21** & **1.53** & **0.37** \\ \hline \(Si\) & **3.40** & 0.04 & **1.52** & **1.42** & **0.47** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(p\)-values (Wilcoxon signed-rank test with Bonferroni–Holm correction) for ratings of distance. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(Em\) & \(As\) & \(Sr\) & \(Si\) \\ \hline \(5.72^{\circ}\) & \(1.57^{\circ}\) & \(1.46^{\circ}\) & \(2.01^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}