# Spatial Sound Rendering Using Intensity Impulse Response and Cardioid Masking Function
## 6 Discussion of Results  
As stated above, the performed listening tests confirmed the subjective quality of the proposed algorithm's performance in terms of its ability to reproduce the position of the apparent sound source in the surrounding space. Cardioid masking functions in this research stage, corresponding to traditional microphone techniques, allowed for an excellent replication of the spatial effects obtained by traditional multi-microphone methods. This ability to reproduce the position can be also confirmed by the waveforms analysis of the actual and synthesized impulse responses for locations #2 and #5 (Figures 10 and 11). Although the individual pairs of channel responses are not identical, in general, the distribution of instantaneous larger amplitudes depicting emerging reflections from the wall surfaces bounding the room coincides. One reason for the discrepancies may be that the cardioid masking functions used are invariant as a function of frequency, which does not coincide with the properties of real microphones. Table 1 shows the correlation between the actual impulse responses from the INA 5 system and the omnidirectional response (from the MK5 microphone) and its change after applying the proposed algorithm. As can be seen, in those channels relative to which the source position is close to the microphone axis (on-axis), the value of the correlation coefficient increases, while for \"rear\" channels relative to the source position, the correlation coefficient decreases. Common-sense trends were appropriate, confirming the correct operation of the algorithm. However, in further research, attention can be focused on how much of this effect is solely due to the amplitude modulation of the initial phase of the impulse response responsible for direct sound and how much of this is due to a change in the ratio in a given channel between correlated direct sound and early reflections and the uncorrelated part of the response associated with diffuse sound and room reverberation. The impulse responses made in this way can then be used in convolution reverberation processors with virtually any number of channels (e.g., [23]). Commercially available convolution reverberation processors use databases that contain impulse responses recorded in actual rooms, generally for only a few positions of excitation signal sources and a few positions of microphones in one or more stereo configurations. Even for the resulting two \begin{table}
\begin{tabular}{c c c} \hline \hline
**Error Interval** & **Method 2** & **Method 3** \\ \hline \(\langle 0,10\rangle\) & 34\% & 67\% \\ \hline \(\langle 10,20\rangle\) & 11\% & 0\% \\ \hline \(\langle 20,30\rangle\) & 22\% & 0\% \\ \hline \(\langle 30,40\rangle\) & 11\% & 11\% \\ \hline \(>\)40 & 22\% & 22\% \\ \hline \(\blacksquare\) (\(0^{\circ},10^{\circ}\)) & \(\blacksquare\) (\(10^{\circ},20^{\circ}\)) & \(\blacksquare\) (\(20^{\circ},30^{\circ}\)) & \(\blacksquare\) (\(30^{\circ},40^{\circ}\)) & \(\blacksquare>40^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Effectiveness of subjective source direction localization for sounds (music only) obtained by the presented methods. Figure 15: Charts of the effectiveness of subjective source direction localization for sounds (music only) based on Table 4.  
channel material, there are many choices, and necessarily, the location of the reverberated sound sources generally does not correspond closely to the position of the sound source when measuring the impulse response. Nevertheless, the results are satisfactory. The approach proposed in the article also requires collecting a certain number of responses from sources distributed around the listener (the more, the better) to create an initial database. However, according to current knowledge, the fusion of directional data obtained from intensity impulse responses and amplitude data from pressure impulse responses is not described in the literature.