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Reproduction of a sound field is a fundamental problem in acoustic signal processing. In this paper, we use a spherical harmonics analysis to derive performance bounds on how well an array of loudspeakers can recreate a three-dimensional (3-D) plane-wave sound field within a spherical region of space. Specifically, we develop a relationship between the number of loudspeakers, the size of the reproduction sphere, the frequency range, and the desired accuracy. We also provide analogous results for the special case of reproduction of a two-dimensional (2-D) sound field. Results are verified through computer simulations.
Ward et al. (Mon,) studied this question.