# Interpolating the Directional Room Impulse Response for Dynamic Spatial Audio Reproduction
## 4 Results and Analysis
### Comparative Analysis in the Classroom
#### 4.1.2 DOA and TOA Error Results  
As introduced at the beginning of Section 4, DOA and TOA errors will be analyzed for the proposed algorithm and other two comparative approaches proposed by [PERSON] and [PERSON], respectively (implemented with the code in [28]). These results for the direct sound and the first five specular reflections in the investigated cases using the real-world and the simulated databases are compared in Figures 6 and 7, separately. The first group of bars in the two figures corresponds to the direct sound, and the second to sixth correspond to the first to fifth extracted specular reflections. Figure 5: Comparison plots of the \(W\) channel of the overall interpolated DRIRs using the proposed algorithm in this paper with the ground truth in row 3 considering: (**a**) the real-world classroom recording; (**b**) the simulated recording. Figure 6: Bar charts comparing the accuracy of the [PERSON]’s method in 2009, the [PERSON]’s method in 2016, and the proposed DRIR interpolation algorithm in the real-world classroom arranged, as shown in Figure 4a, including: (**a**) the error of azimuth and elevation; (**b**) the error of TOA. All errors are calculated as the absolute difference between the interpolated signal and the ground truth for regular spacing cases in row 3, row 5, and row 8, as well as irregular spacing cases in row 7 and column 9, respectively (from top to bottom in each subplot). Figure 7: Bar charts comparing the accuracy of the [PERSON]’s method in 2009, the [PERSON]’s method in 2016, and the proposed DRIR interpolation algorithm in the simulated classroom arranged as shown in Figure 4a, including: (**a**) the error of azimuth and elevation; (**b**) the error of TOA. All errors are calculated as the absolute difference between the interpolated signal and the ground truth for regular spacing cases in row 3, row 5, and row 8, as well as irregular spacing cases in row 7 and column 9, respectively (from top to bottom in each subplot). When looking at the error of the interpolated DOA, the proposed DRIR interpolation algorithm shows, generally, the smallest average errors of the azimuth and elevation in all sub-figures amongst the three approaches, which means the most accurate extractions of DOA information of the direct sound and specular reflections for synthesizing overall interpolated signals at the target listening position in both the real-world and the simulated classrooms. This advantage is particularly obvious in the simulation, where almost all errors in the first four cases using the proposed method are close to zero, with small errors of nearly five degrees appearing in column 9. The [PERSON]'s approach shows strength in interpolating for column 9 in the real world, presenting the smallest errors of azimuth and elevation estimation for nearly all of the direct sound and specular reflections. The [PERSON]'s method and the [PERSON]'s method generally show similar errors for the azimuth and elevation in Figures 6 and 7, whereas in column 9 for both databases, the [PERSON]'s method leads to larger errors. As for the TOA error of the direct sound and specular reflections compared with the ground truth, the two comparative methods generally present equivalent TOA errors in the real-world classroom, with the proposed DRIR interpolation method showing slightly lower TOA errors. The [PERSON]'s method leads to slightly large errors in Figure 6b, especially for row 5 and column 9, where the errors of late reflections can reach 600 samples, i.e., 600/96,000 = 6.25 ms. In the simulation, [PERSON]'s algorithm suffers from large TOA errors at a few peaks (e.g., peaks 5 and 6 in the row 5 case of Figure 7b). [PERSON]'s method also shows large TOA errors at a few peaks (e.g., peaks 5 and 6 in the column 9 case of Figure 7b). The proposed approach has, in general, the lowest errors, whereas it also shows a large error at peak 6 in column 9 in the case of Figure 7b.