Loudness stability of binaural sound with spherical harmonic representation of sparse head-related transfer functions

In response to renewed interest in virtual and augmented reality, the need for high-quality spatial audio systems has emerged. The reproduction of immersive and realistic virtual sound requires high resolution individualized head-related transfer function (HRTF) sets. In order to acquire an individualized HRTF, a large number of spatial measurements are needed. However, such a measurement process requires expensive and specialized equipment, which motivates the use of sparsely measured HRTFs. Previous studies have demonstrated that spherical harmonics (SH) can be used to reconstruct the HRTFs from a relatively small number of spatial samples, but reducing the number of samples may produce spatial aliasing error. Furthermore, by measuring the HRTF on a sparse grid the SH representation will be order-limited, leading to constrained spatial resolution. In this paper, the effect of sparse measurement grids on the reproduced binaural signal is studied by analyzing both aliasing and truncation errors. The expected effect of these errors on the perceived loudness stability of the virtual sound source is studied theoretically, as well as perceptually by an experimental investigation. Results indicate a substantial effect of truncation error on the loudness stability, while the added aliasing seems to significantly reduce this effect.