# 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
Moreover, due to the ideal configuration of the simulated classroom, the distribution pattern across the six components for each method in all subplots of Figure 7 look similar. These results obtained in the classroom present performances of the three comparative DRIR interpolation methods in a smaller room. It can be observed that, generally, the closer the microphones are located to the sound source, the larger the DOA and TOA errors are. Note that here we have evaluated the two limited scenarios using conventional weighted-average interpolation approaches, such as the [PERSON]'s approach, where the source is close to both known recording positions (row 3) as well as the source being closer to one recording position than to the other (row 7 and column 9). The proposed method in these cases shows reduced errors compared to the traditional linear method designed by [PERSON], which indicates that the limits of large localization errors mentioned in [5] is mitigated by the proposed scheme. Additionally, an error measurement of direct-to-reverberant ratio (DRR) is introduced to describe acoustic characteristics of signals and to evaluate the accuracy of the proposed interpolation algorithm by assessing the difference between the interpolated and the known recording signals. The DRR is defined as the ratio of energy between the direct sound and all of the reverberant signals, formulated as \(DRR=10\times log10\frac{\left(X(T_{0}-C\cdot T_{0}+C)\right)^{2}}{\left(X(T_{0 }+C+1\times med)\right)^{2}}\)[29], where \(X\) is the sampled signal to be evaluated, \(T_{0}\) represents the occurring time (in terms of the number of samples) of the direct sound in the recording, and \(C\) is the number of samples to define the range of time of the whole direct sound signal. (\(C\) should be equivalent to 2.5 ms according to [30]) \(X(T_{0}-C:T_{0}+C)\) means the snippet of signal \(X\) from Sample \(T_{0}-C\) to Sample \(T_{0}+C\), which is expressed in MATLAB code and so is \(X(T_{0}+C+1:end)\). The DRR in this paper is implemented with the code in [29]. The DRR errors in the real-world and simulated classrooms using three interpolation approaches developed by [PERSON] [16], [PERSON] [4], and the authors of this paper are compared in Table 1. The overall errors are calculated by averaging DRR differences (absolute value) between the interpolated DRIR and the ground truth in all five investigated scenarios. It can be found that in both the real-world and simulated classrooms, the [PERSON]'s method obtains the most accurate DRRs, followed by the proposed method. The reason may lie in the limits of accuracy in the signal decomposition process of the proposedmethod in the classrooms. Future work will investigate whether or not the errors lead to a significant difference in the perception of the spatial properties of the sound scene. Combining all these experimental evaluations of the directional information and time delay of the direct sound and specular reflections, the proposed method shows generally the most accurate results when interpolating the DRIR at selected listening positions in both the real-world and simulated classrooms.