Sound field synthesis reproduction techniques such as wave field synthesis can accurately reproduce wave fronts of arbitrary curvature, including sources with the wave fronts of a source in front of the array. The wave fronts are accurate up until the spatial aliasing frequency, above which there are no longer enough secondary sources (loudspeakers) to reproduce the wave front accurately, resulting in spatial aliasing contribution manifesting as additional wave fronts propagating in directions other than intended. These contributions cause temporal, spectral, and spatial errors in the reproduced wave front. Focused sources (sources in front of the loudspeaker array) have a unique attribute in this sense in that there is a clearly defined region around the virtual source position that exhibits no spatial aliasing contributions even at an extremely high frequency. This paper presents a method for the full characterization of this un-aliased region using both a ray-based propagation model and a time domain approach.
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