Robust Two-Dimensional Surround Sound Reproduction for Nonuniform Loudspeaker Layouts

The design of panning functions for surround sound systems with nonuniform loudspeaker layout is considered. It is shown that theoretical solutions exist which are interpolants for nonuniform sampling of periodic functions. However, these solutions produce large interference effects for positions far from the array center, and they are sensitive to phase and magnitude mismatches between loudspeakers. Robust solutions approximate a double complementarity property in which the weights and squared weights sum to 1 for each source angle. A least-squares method is developed for developing robust panning functions which produces a more consistent sound-field directionality than those produced by matching parameters at the origin.