## 2 Proposal of a Position-Dynamic Binaural Synthesis System
### Spatial Sub-Sampling  
In the exemplary audio system, the different BRIR data sets, which are required for the listener's movement in the room, are created for predefined discrete areas in the room. These areas are called cells. The totality of all cells is called grid. Depending on the chosen spatial resolution, a BRIR data set is valid for one of these cells. A BRIR data set consists of BRIRs for the left and right ear for all available head orientations and for one audio object. Only in the center of this area, the BRIR data set corresponds to a correct mapping of distance and direction to the sound source. Towards the edges, the deviation of direction and distance cues and thus the reproduction error increases. If the spatial resolution is chosen to be low, perceptible errors will increase. The shapes of these cells can be uniform in the sense of a position-independent shape, for example, quadratic. However, the shapes of the cells can also be nonuniform in the sense of a position-dependent shape. The use of a uniform grid is not very good at taking perceptive inaccuracies in localization [27] and distance perception [28; 29] into account. Furthermore, it was shown that for a range of signal types a uniform positional BRIR grid requires a 5 cm resolution  
Figure 2: Block diagram of a specific position-dynamic binaural synthesis system including the provision of BRIRs in the room (100), filter creation (120), and real-time processing (130). The separated blocks on the right indicate input data to blocks on the left side. The descriptions in the text refer to the several blocks indicated by the number of each block. or higher to provide a smooth transition without noticeable discontinuities [26]. If the listener is very close to the virtual audio object, a high spatial resolution must be selected to minimize perceptional errors. However, this high resolution is unnecessary at greater distances from the source which allows a reduction of the required number of BRIRs. The approach which is discussed here is called Maximum Allowed Error Method (MAEM) and was developed by [PERSON] and [PERSON] [30]. The MAEM (see block 100 in Figure 2) describes a method to parameterize the size and shape of an area in the listening room which is represented by one BRIR data set. The parameterization is motivated by perceptual thresholds in spatial hearing. Figure 3 shows the principles of localization blur and distance blur in the horizontal plane. If a sound source is perceived from a certain direction and distance, the acoustic position of this sound source can change within certain limits without changing the perception of direction and distance. The displacement is inaudible. In a similar way, other sound sources located in this range are perceived from the same direction and distance. The size of this range is determined by the just noticeable differences (JNDs) for direction and distance perception of the direct sound of the source. If a fixed localization blur or minimum audible angle (e.g., 5\({}^{\circ}\)) is assumed, the density of the cells (in the sense of the width of the cells) should increase at small distances to the source and decrease at larger distances. The situation is similar regarding distance blur. For small distances, the density (in the sense of the length of the cells) should be higher than for large distances. This approach leads to a grid of nonuniform cells which can effectively reduce the number of BRIRs required without causing increased errors in direction and distance perception. An extension of this approach could also consider the reflections to determine the JND and not only the direct sound. The maps generated by the MAEM approach are based on a Voronoi diagram (Figure 4). First, a floor plan of the room can be loaded as 1 bit graphic (blocks 101 and 161 in Figure 2). In the immediate proximity of the walls, the calculation of the cells can be influenced by specifying a minimum wall distance (162).