Investigation of sweet spot radius of sound reconstruction system based on inverse filtering

Abstract

Sound field reconstruction techniques are very effective tools for a sound system of live-viewing or acoustical design in architecture. In the live-viewing system, listeners can enjoy highly realistic sound through the system. In addition, the system would allow acoustical designers to evaluate a sound field calculated in architectural spaces before their completion. There are several methods aiming at sound field reconstruction, such as Higher-order Ambisonics (HOA), Wave Field Synthesis (WFS), and Boundary Surface Control (BoSC). It is important to reconstruct a sound field within a broad region in order to allow a listener to look around or to move, or to allow multiple listeners to experience the sound field at the same time. To reconstruct a sound field in a broad region, it is necessary to employ lots of microphones and loudspeakers. It is becoming easier and less expensive to handle many devices due to the progress of computer technologies and network audio technologies. The reconstruction region of a sound field is called a sweet spot, which is defined as an area in which a normalized reconstructed error (NRE) would be smaller than 4%, for an example. HOA is a method to reconstruct a sound field using the spherical harmonics expansion. It is known that a radius of sweet spot in HOA is proportional to an expansion order. In the BoSC system, both sound pressure and particle velocity on the boundary surface of a reconstruction region are to be controlled using inverse filters to reconstruct a sound field. While the BoSC system aims to reconstruct a sound field in a region surrounded by boundary surface, some researchers suggest that a sweet spot would be formed outside of this controlled region. The authors numerically investigated the radius of sweet spot for the BoSC system which consisted of a spherical controlling surface and a spherical loudspeaker array. The spherical loudspeaker array and spherical microphone array were employed in the numerical simulation. The radius of the spherical loudspeaker array was 2.5 meters and the number of loudspeakers was 122. The loudspeakers were mounted at the vertices of the geodesic polyhedron. The number of microphones was varied from 16 to 256 and the radii of the microphone array was varied from 0.05 meters to 0.20 meters. The microphones were located at the positions calculated from the Fibonacci spiral. The results showed that the radii of the microphone array, within which the sound field would be reconstructed accurately in theory, do not affect the radii of sweet spot, but the number of the microphones could be related to the radii of sweet spot. Furthermore, the radii of sweet spot is inversely proportional to the frequency. These results indicated that the relation between the radii of sweet spot and the number of microphones in the BoSC system is likely parallel to that of the HOA system. In general, the BoSC system could be realized by simplified control of only sound pressures except for resonance frequencies of the corresponding internal Dirichlet problem. However, the results also suggested that this simplification could have an impact on the radius of sweet spot.