Reproduction of a plane-wave sound field using an array of loudspeakers

Reproduction of a sound field is a fundamental problem in acoustic signal p rocessing. In this paper, we use a spherical harmonics analysis to derive p erformance bounds on how well an array of loudspeakers can recreate a three -dimensional (3-D) plane-wave sound field within a spherical region of spac e. Specifically, we develop a relationship between the number of loudspeake rs, the size of the reproduction sphere, the frequency range, and the desir ed accuracy. We also provide analogous results for the special case of repr oduction of a two-dimensional (2-D) sound field. Results are verified throu gh computer simulations.