Localization in Wave Field Synthesis and higher order Ambisonics at different positions within the listening area Hagen Wierstorf 1 , Alexander Raake 1 , Sascha Spors 2 Email: hagen.wierstorf@tu-berlin.de 1 Assessment of IP-based Applications, Technische Universit¨ at Berlin, 10587 Berlin, Deutschland 2 Institute of Communications Engineering, Universit¨ at Rostock, 18119 Rostock/Warnem¨ unde, Deutschland Introduction Sound field synthesis methods try to synthesize a desired sound field within an extended listening area. If this task can be complied, the perception of a listener placed within the listening area will not differ from his/her au- ditory perception within a real sound field. Due to the practical limitation in the number of loudspeakers than can be applied for sound field synthesis methods, the pro- duced sound field is in most cases only indistinguishably from the real sound field in a small area and/or under a certain frequency. This study investigates the ability to correctly localize sources in a synthesized sound field for two sound field synthesis methods. These methods are Wave Field Syn- thesis [1] and near-field compensated higher order Am- bisonics [2]. In order to investigate the localization by the listeners in the whole listening area, the area was sampled at 16 different positions. To further investigate on the number of loudspeakers used, three different loud- speaker arrays with different spacings of the single loud- speakers were used. The different listener positions and loudspeaker arrays were presented to the subjects via dy- namic binaural synthesis [3]. This has the advantage of seamlessly switching between the different conditions and reliably placing of the different listeners at exactly the same places. In a former test it was shown that dynamic binaural synthesis has no influence on the localization performance [5]. In the next chapter a brief introduction into Wave Field Synthesis and near-field compensated higher order Am- bisonics will be given, with a highlight on the differences between the two methods. Afterwards a localization ex- periment will be introduced and its results will be pre- sented and discussed. Wave Field Synthesis and near-field com- pensated higher order Ambisonics In sound field synthesis methods one is looking for solu- tions to the following equation. P (x,ω)=  xn∈∂V G(x|x n ,ω)D(x n ,ω) , (1) where G(x|x n ,ω) denotes the sound field that originates from a single loudspeaker placed at x n on the boundary ∂V of a volume V , and D(x n ,ω) is the signal that is fed into the loudspeaker. P (x,ω) is the desired sound field we targeting to create in V . The equation has to be solved with respect to D(x n ,ω). For special geometries like a circle or a sphere this can be done directly and results in a solution known as near- field compensated higher order Ambisonics, if we assume a point source like characteristic for a single loudspeaker. In this case the sound field is represented by circular or spherical harmonics. If we sample the boundary with M loudspeakers, only sound fields represented by harmonics up to an order of N = M−1 2 can be synthesized correctly for a circular array. In Wave Field Synthesis the equation is solved by a high frequency approximation that solves the problem for small linear array elements. Applied to a circular array this leads to a selection of an active sub-array for a given source. This is illustrated in Fig. 1a, where the sound field of a plane wave coming from above is synthesized as the desired sound field. The plane wave has a frequency of 2 kHz. In addition to the difference in the active loud- speakers there is also a difference in the artifacts that are present in the synthesized sound field with discrete loud- speakers. The loudspeaker array has a spacing of 0.17 m between its loudspeakers which enables only a correct re- production of frequencies up to 1 kHz. For Wave Field Synthesis theses artifacts vanish for positions farer away from the array, whereas for near-field coming higher or- der Ambisonics there is always a artefact-free region in the center of the array – compare Fig. 1a and Fig. 1b. In the next section a localization experiment is presented that investigates the influence of the different proper- ties of Wave Field Synthesis and near-field compensated higher order Ambisonics on the perception of the direc- tion of a desired source. Method For both sound field synthesis methods the same circular loudspeaker array with a diameter of 3 m was used. The array consisted of 56, 28, or 14 loudspeakers, correspond- ing to spacings of 0.17 m, 0.34 m, and 0.67 m between the loudspeakers. Within the loudspeaker array 16 different listening positions were chosen as shown in Fig. 1c. All the positions were only in the left half of the listening area due to the symmetry of the problem. Both sound field synthesis methods synthesized the field of a point source located at (0, 2.5)m and a plane wave traveling into the direction (0, -1). For Wave Field Syn-