## 2 Proposal of a Position-Dynamic Binaural Synthesis System
### BRIR Synthesis
#### 2.2.3 Sound Source Directivity  
For both presented approaches of creating BRIRs for additional listening positions, an adequate modeling of the direct sound with its directivity is essential, as it is also relevant for the progress of the DRR within a given listening area. The shaping of the ITDG described in Section 3.2.3 does not include a correct representation of the sound source directivity (SSD) pattern. The BRIRs of the measured position contain the directional characteristics of the sound source at that position. If these BRIRs are used to synthesize another position in the room, the directional characteristics remain unchanged. A correction is therefore desirable, to minimize the physical and the perceived differences between the measured and synthesized BRIRs. This is expected to result in a more plausible listening experience.  
The shaping algorithm is therefore enhanced in a further implementation and study. An additional processing step to consider the SSD is shown in Figure 8. A predefined source-directivity pattern of the sound source used for the measurements is taken into account to vary the direct sound part of the BRIRs. In this setup, a Geithain MO-2 loudspeaker is used for the measurements. The frequency and angular-dependent changes in the amplitude for different orientations are adopted for the calculations of the extrapolated BRIRs. For that, the algorithm determines the angular relation between the position of the loudspeaker to the measurement position and to the synthesis position. The amplitude of the direct sound part of the BRIR at the position to be synthesized is then boosted or attenuated according to the change in amplitude in the pattern between these angles. Additionally, the inverse distance law is applied to take care of the different distances to the position of the loudspeaker. Further details are described in [33].  
The evaluation of physical parameters shows an improvement in the deviation of the direct to reverberation energy ratio (DRR) between a measured reference BRIR and the synthesized BRIR considering the SSD in comparison with BRIRs not considering the SSD. Figure 9 shows a heat map to display the deviations. In an investigation using the position \"D1\" for measurement for the most synthesized positions deviations smaller than 2 dB are reached. Especially for the positions off-axis to the sound source, an improvement is seen. However, the reduction of the DRR deviation is in a range from 0.5 dB to around 4 dB dependent on the difference between the synthesized and measured position. The deviations are mostly within the JND for the examined DRR range and therefore are not perceptible.  
Even though good results for the DRR deviations are reached, there is still room for improvement. The perceived differences, shown in Section 3.2.3, are probably based on other physical parameters. Further research should, for example, investigate whether changes of the first reflections and the reverberant parts of the BRIRs due to SSD need to be considered for the calculations as well to address spatial perception and coloration effects in more detail.  
Figure 8: Block diagram of the synthesis chain to include directivity patterns in the ITDG-shaping approach.