## 4 Results  
### Smoothing the Magnitude Spectra of Direct Parts in BRIRs  
Figure 8 shows the mean externalization ratings of the test stimuli for the \"SN\" (diamonds), \"SL\" (triangles), \"SR\" (circles), and \"SB\" (squares) conditions in different azimuth angles. In general, the externalization ratings increased as the sound source moved from frontal to lateral incidence angles for all conditions. In the case of non-processed BRIRs (\"SN\" condition), the overall mean externalization ratings were high across different azimuth angles (between 2.2 and 2.8), corresponding to the sound sources being well externalized and very close to the loudspeakers' positions and were clearly higher than those for the other three (\"SB\", \"SL\", and \"SR\") conditions.  
For the \"SB\" condition, the mean externalization ratings were below 1.0 for azimuth angles of 0\({}^{\circ}\) and \(\pm\)30\({}^{\circ}\), corresponding to sound sources being fully internalized (\"in the head\"). The sound images were perceived as close to subjects' heads or slightly externalized for \(\pm\)60\({}^{\circ}\) and \(\pm\)90\({}^{\circ}\) sound sources. For azimuth angles of \(-\)60\({}^{\circ}\) and \(-\)90\({}^{\circ}\), the externalization ratings were higher for the \"SR\" condition than the \"SB\" and \"SL\" conditions, while the externalization ratings for the \"SL\" condition  
Figure 8: Mean externalization ratings from zero (the sound is in my head) to three (the sound is externalized and at the position of the loudspeaker) across listeners for the “SN” (diamonds), “SL” (triangles), “SR” (circles), and “SB” (squares) conditions in different azimuth angles. The error bars indicate the standard deviations of the mean values.  
were higher than those for the \"SB\" and \"SR\" conditions in the case of 60\({}^{\circ}\) and 90\({}^{\circ}\) sound sources. In addition, the externalization ratings for the \"SL\" and \"SB\" conditions were almost the same in the case of negative azimuth angles, while the ratings for the \"SR\" and \"SB\" conditions were almost identical for positive azimuth angles. No substantial difference in externalization ratings was observed among the three (\"SL\", \"SR\", and \"SB\") conditions for azimuth angles of 0\({}^{\circ}\) and \(\pm\)30\({}^{\circ}\).  
For each azimuth angle, an analysis of variance (ANOVA) with post-hoc-test (5% significance level with Bonferroni adjustment) was performed to show the significant differences of externalization ratings among the \"SN\", \"SL\", \"SR\", and \"SB\" conditions. Overall, consistent with the visual inspection of Figure 8, the results for the \"SN\" condition differed significantly from the results for the other three conditions across various azimuth angles (\(p\ll 0.05\)). In the case of azimuth angles of 0\({}^{\circ}\) and \(\pm\)30\({}^{\circ}\), no significant difference was observed among the \"SL\", \"SR\", and \"SB\" conditions (\(p>0.2\)). For lateral sound sources located at \(-60^{\circ}\) and \(-90^{\circ}\), the results for the \"SR\" condition differed significantly from the results for the \"SL\" and \"SB\" conditions (\(p\ll 0.05\)), while there was no significant difference between the externalization ratings for the \"SL\" and \"SB\" conditions (\(p>0.3\)). In the case of 60\({}^{\circ}\) and 90\({}^{\circ}\) sound sources, there was no significant difference between the externalization ratings for the \"SR\" and \"SB\" conditions (\(p>0.3\)), but each differed significantly from the results for the \"SL\" condition (\(p\ll 0.05\)).