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Characterization of Spherical Loudspeaker Arrays

The synthesis and rotational control of radiation patterns produced by spherical arrays of loudspeakers is studied. We identify operating regions, in terms of complexity of patterns and frequency ranges, over which patterns can be accurately synthesized. By considering an inner product space of far-field patterns, we can reason geometrically about approximation errors when using the systems to synthesize and control target responses. Bounds for normalized error across subspaces, in particular subspaces corresponding to the control operation of rotation, are calculated using singular value decomposition. The bounds can be interpreted as the best and worst case errors encountered when dynamically steering the patterns.

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