Revisiting the theory of auditory displays based on the virtual sphere model

Virtual Auditory Displays (VADs) are used to present realistic spatial sound. High-quality VADs must account for three factors: individuality (Head-Related Transfer Function), room acoustics (Room Transfer Function) and freedom of motion (active listening). The Auditory Display based on the VIrtual SpherE model (ADVISE) was proposed to simplify the problem by dividing it, through the Kirchhoff-Helmholtz integral theorem, into 1) a listener-free room acoustics simulation and 2) a free-field VAD using HRTFs. Users of ADVISE can move freely within the free-field region, thus accounting for active listening. This paper revisits the classic theory of ADVISE and identifies three oversights in the original proposal: 1) The ADVISE formulation suffers from non-unique boundary conditions at some frequencies. 2) The original proposal re-creates a set of boundary conditions using secondary sources that diverge on the boundary itself. 3) Considerations for sound propagation are absent in the original formulation. Two new formulations that retain the philosophy of ADVISE but are free from these problems are presented. The first one is based on the theory of Boundary Matching Filters, while the second is inspired by High-Order Ambisonics. The latter is found to be better suited for applications where freedom of motion is important since the presented sound field can be shifted by a translation matrix.