# Interpolating the Directional Room Impulse Response for Dynamic Spatial Audio Reproduction
## 5 Conclusions  
This paper has proposed an approach of DRIR interpolation for dynamically reproducing spatial audio with limited data. The DRIR is firstly represented or measured in B-format at fixed numbers of known positions. By utilizing two of these known DRIRs for each interpolation, the proposed algorithm separates the DRIR into two parts, the specular reflection (including the direct sound) and diffuse signals. A few early specular reflection signals are then further decomposed into estimated image source components and their corresponding DOAs (azimuth and elevation). Through interpolating the reflection components and the DOA at two measured positions, the useful information for reproducing the acoustic characteristic at any new position within the recording region can be obtained by synthesizing a known DRIR with the interpolated results, although this region is restricted to within the cover of available recordings due to the interpolation nature of the method. Experiments are conducted by utilizing existing real-world recordings and our simulated recordings of the DRIR, which were designed to use the two closest recordings for interpolation, but here we have investigated broader cases with different source-to \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Great Halls**} & \multicolumn{1}{c}{**Error—Tylka**} & \multicolumn{2}{c}{**Error—Southern**} & \multicolumn{1}{c}{**Error—Proposed**} \\ \hline \multirow{6}{*}{real-world} & row 4–1 m & 6.92 & 0.12 & 0.29 \\  & row 4–2 m & 5.99 & 0.88 & 1.47 \\  & row 4–3 m & 5.84 & 1.59 & 0.62 \\  & row 9–1 m & 7.11 & 0.68 & 0.33 \\  & row 9–irregular & 7.36 & 0.68 & 0.61 \\  & diagonal & 12.65 & 0.49 & 1.75 \\ \cline{2-5}  & average & 7.65 & 0.74 & 0.85 \\ \hline \multirow{6}{*}{simulated} & row 4–1 m & 20.20 & 0.69 & 0.08 \\  & row 4–2 m & 23.75 & 0.03 & 1.02 \\  & row 4–3 m & 17.97 & 1.11 & 1.22 \\  & row 9–1 m & 2.27 & 1.10 & 0.70 \\  & row 9–irregular & 2.29 & 1.15 & 1.25 \\  & diagonal & 7.10 & 3.18 & 3.38 \\ \cline{2-5}  & average & 12.26 & 1.21 & 1.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of DRR errors in the real-world and simulated great halls (unit: dB). microphone and microphone-to-microphone spacing for a thorough evaluation. Results indicate that the proposed algorithm presents the most accurate interpolated azimuth and elevation, whilst leading to the least TOA error compared with two previous representative approaches [4; 16], and it works very well in a small room with an average RT (the classroom in this paper). This means the reflections in the resulting DRIR signal can be recovered precisely in terms of their directions and occurring time, which are the key to guaranteeing the DRIR interpolation accuracy and are the focus of this work. From the grid-based experiments in the same row with different regular spacing between two recorded positions, we also find that different microphone-to-microphone distances do not affect the DOA estimation accuracy much, but the TOA error is much smaller when the distance is small. Moreover, the proposed approach shows reduced errors in two limited scenarios for conventional weighted-average interpolation methods [5]. When the listening position and known recorded points are close to the source, the conventional method from Southern [4] suffers from large errors in terms of azimuth estimation, whilst the proposed method obtains nearly zero errors in most such cases. As for scenarios of irregular spacing where the source is closer to one microphone than to the other, the proposed algorithm also obtains the most accurate estimation of the DOA and TOA among all comparative approaches. However, the errors of DOA estimation in the simulated great hall using the proposed method with irregular spacing can be large for a few specular reflections, which will cause distortions to the interpolated DRIR and affect the perception of the reconstructed spatial audio to some extent.