Joint sampling theory and subjective investigation of plane-wave and spherical harmonics formulations for binaural reproduction

With the recent proliferation of spherical microphone arrays for sound field recording, methods have been developed for rendering binaural signals from these recordings and free-field head related transfer functions (HRTFs). Employing spherical arrays naturally leads to methods that are formulated in the spherical harmonics (SH) domain, using order-limited SH representations. However, the incorporation of HRTFs and enclosed sound fields typically leads to methods that are formulated in the space domain using plane-wave (PW) representation. Although these two representations are widely used, the current literature does not offer a complete theoretical framework to derive sampled PW representation from the SH representation in the context of binaural reproduction and sound perception. This paper develops a mathematical framework showing that when specific conditions for the joint sampling of the sound field and the HRTFs are maintained, sampled PW representation can be derived from the SH representation without error, and the resulting binaural signals are independent of the employed spatial sampling scheme. Furthermore, analysis of the aliasing error shows that the sound field is more sensitive to aliasing than the HRTFs. The theoretical analysis is complemented by a listening experiment, in which both PW and SH representations are perceptually evaluated for different spatial sampling schemes, SH orders, and levels of aliasing when deviating from the joint sampling conditions.