Effect of discretization on off-axis listeners in binaural synthesis based on the optimal source distribution

3D sound reproduction based on binaural synthesis over loudspeakers is one of the most important techniques in immersive spatial audio. The system inversion involved in the binaural synthesis gives rise to several problems such as dynamic range loss, distortion of the reproduction transfer function, and a lack of robustness to room reflections. The principle of Optimal Source Distribution was proposed to overcome these problems. This utilizes a pair of conceptual monopole transducers whose azimuthal location varies continuously as a function of frequency. Another potential of the principle is that it can provide listening positions for multiple off-axis listeners, in addition to the on-axis listener whose inverse matrix is given, since the phase interference state is aligned at all frequencies. However, these continuously varying transducers are too conceptual to realize in practice. It is necessary to provide discretized sound sources with appropriate frequency ranges according to the principle. In this paper, the effect of discretization of the principle on off-axis listeners' performance is numerically investigated to reveal how those off-axis sweet spots are formed as the discretization becomes finer. An experiment is also carried out using an actual discretized system and the effect of the head-related transfer functions is considered.