Abstract
Starting from the uniform spatial sampling theorem, a nonuniform spatial sampling theorem is developed for single-frequency acoustic fields. Using these two theorems, it is shown that, if a processing operation is known which maximizes a criterion C for the outputs of one array of spatial sampling points, then the equivalent processing operation, which maximizes C for the outputs of a different array of spatial sampling points, can be found using the uniform and nonuniform spatial sampling functions. The utility of this result is to permit direct computation of the processing operation maximizing C for a point array of unusual or complicated shape, starting from a point array for which the processing operation maximizing C is simple. Examples include a demonstration of superdirectivity as the equivalent processing operation for usual pattern formation of half-wavelength spaced point arrays, a qualitative comparison of surface versus volumetric array processing, and connection with recent work of Cron and Marsh.
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