Optimal Spatial Sampling of Plant Transfer Functions for Head-Tracked Personal Sound Zones

The implementation of head tracking in personal sound zone (PSZ) reproduction was investigated in terms of the optimal spatial resolution required for sampling the plant transfer functions, which results from a trade-off between the measurement effort and the robustness of isolation performance against head movements. The plant transfer functions of an experimental PSZ system were densely measured along translational moving trajectories of a dummy head, and then downsampled to different resolutions at which the PSZ filters were computed and the isolation performance was numerically simulated. By analyzing the variation in the isolation performance, the optimal sampling resolution, above which a given minimum level of isolation can be maintained over the reproduction area, was determined as a function of head position and frequency for two separate zones. It was found that the optimal spatial sampling resolution is in general inversely proportional to the distance between the two listeners, and to that between the moving listener and the loudspeaker array. Moreover, the high-frequency part of the plant transfer functions was found to require a higher sampling resolution than the low-frequency part, while a moving bright zone requires a lower sampling resolution than a moving dark zone.