Three-Dimensional Sound Field Reproduction Based on Weighted Mode-Matching Method

Abstract

A sound field reproduction method based on the spherical wavefunction expansion of sound fields is proposed, which can be flexibly applied to various array geometries and directivities. First, we formulate sound field synthesis as a minimization problem of some norm on the difference between the desired and synthesized sound fields, and then the optimal driving signals are derived by using the spherical wavefunction expansion of the sound fields. This formulation is closely related to the mode-matching method; a major advantage of the proposed method is the optimal weight on the mode determined according to the norm to be minimized instead of the empirical truncation in the mode-matching method. We also provide some examples of norms and their corresponding weights in analytical forms. Both interior and exterior sound field reproduction are considered in the proposed method, and some applications, such as multizone reproduction and interior reproduction with exterior cancellation, are also discussed. Numerical simulation results indicated that higher reproduction accuracy can be achieved by the proposed method than by the current pressure-matching and mode-matching methods.