## 3 Experimental Analysis
### Directional Decays and Dominant Reflection Directions  
As we discussed in Section 3.1.1, decay times are a function of frequency and direction. Additionally, from Section 3.3, we found that the modes with higher decay times can be different from the modes with high reflection powers. Therefore, a more comprehensive analysis of the spatial spectrum of these reflections is necessary to identify room surfaces causing the observed behaviors for the frequencies of interest. Figure 11a,b shows the directional decay times of Room-1 for \(\mathbf{y}_{o}=(1,90^{\circ},40^{\circ})\) and \(\mathbf{y}_{o}=(1,90^{\circ},120^{\circ})\), respectively, obtained from the 60 dB decay time of \(P_{R}(t,k,\mathbf{y}|\mathbf{y}_{o})\) in each \(\mathbf{y}\) direction. Figure 12a,b \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**In Room**} & \multirow{2}{*}{**Source Position**} & \multirow{2}{*}{\begin{tabular}{c} **Maximum Decay** \\ **Time (s)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Frequency (Hz) with** \\ **Maximum Decay Time (s)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Average** \\ **Decay Time (s)** \\ \end{tabular} } \\ \cline{3-4} \multirow{3}{*}{Room-1} & \(\mathbf{y}_{o}=(1,90^{\circ},40^{\circ})\) & 0.4114 & 140 & 0.2822 \\ \cline{2-4}  & \(\mathbf{y}_{o}=(1,90^{\circ},120^{\circ})\) & 0.4540 & 164 & 0.2899 \\ \cline{2-4}  & \(\mathbf{y}_{o}=(1,90^{\circ},200^{\circ})\) & 0.4823 & 140 & 0.2995 \\ \cline{2-4}  & \(\mathbf{y}_{o}=(1,90^{\circ},280^{\circ})\) & 0.4398 & 258 & 0.2936 \\ \hline \multirow{4}{*}{Room-2} & \(\mathbf{y}_{o}=(1,90^{\circ},0^{\circ})\) & 1.1349 & 492 & 0.8133 \\ \cline{2-4}  & \(\mathbf{y}_{o}=(1,90^{\circ},90^{\circ})\) & 1.1066 & 328 & 0.8288 \\ \cline{1-1} \cline{2-4}  & \(\mathbf{y}_{o}=(1,90^{\circ},180^{\circ})\) & 1.0498 & 328 & 0.8341 \\ \cline{1-1} \cline{2-4}  & \(\mathbf{y}_{o}=(1,90^{\circ},270^{\circ})\) & 1.0640 & 586 & 0.8182 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum and average decay times in Room-1 and Room-2. Figure 10: Decay time with frequency for different source positions in Room-2. Figure 9: Decay time with frequency for different source positions in Room-1. shows the directions with high reflection powers in Room-1 for \(\mathbf{y}_{o}=(1,90^{\circ},40^{\circ})\) and \(\mathbf{y}_{o}=(1,90^{\circ},120^{\circ})\), respectively. The letters indicated near the locations of highest reflection powers in Figure 12 are coarsely mapped onto the real Room-1 environment in Figure 13. As evident from this figure, the locations around 'A', 'C', 'D', and 'E' have glass surfaces with high reflectivity, and hence the observed dominant power directions are valid. Furthermore, there is no evident pattern between the distributions in Figures 11 and 12 for the given modal frequencies, and hence the feature predictions based on computational room acoustic models can be imprecise. In such cases, we can employ the proposed technique to reproduce authentic spatio-temporal room responses. According to Figures 11 and 12, the directions of high decay times and dominant reflections are different from each other for every frequency and source position. Even though the dominant reflection locations and directional decay distribution have many common factors of influence, the reflection power in a direction strongly depends on the source directivity and source-to-wall distance, whereas the directional decay is mainly a function of the wall impedance coefficients and reflection paths. Hence, as seen in Figure 11, the directional decay will be different between the frequencies due to wall impedance variations, as well as for different source positions due to change in reflection path. In contrast, if we observe Figures 12 and 13, the dominant reflection locations 'A', 'B', and 'C' have similar azimuth values and source-to-wall distance when the source is at \(\mathbf{y}_{o}=(1,90^{\circ},40^{\circ})\).