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Only Planar and Spherical Arrays Can Work Perfectly

It is well known that only spherical waves propagate in 3D without a wake, which includes plane waves as a limiting case. A line array produces a cylindrical wave, which has a wake (Morse and Ingard, 1968, p. 243). This takes the form of temporal dispersion behind the wavefront in the soundfield reconstruction from linear arrays. Interestingly, nobody seems to complain about it, so it can't be a particularly audible distortion. However, for best results, planar (or spherical) sample distributions are preferred.

Another disadvantage of cylindrical waves relative to plane waves is amplitude decay by $ 1/\sqrt{r}$ (consider energy conservation), where $ r$ is distance from the cylinder axis. This is less of a problem, since it preserves audio fidelity and spatial locations, and is potentially even desirable since it gives the listener a way to alter listening level by merely moving closer to or farther from the array (-3dB per distance doubling).

We will continue to consider primarily linear arrays, in which soundfield reconstruction from samples happens only along the left-right dimension, and VBAP or stereo is used for the vertical dimension, if anything. There will be other approximation errors as well, and the key question as always is the audibility of those errors.

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``A Spatial Sampling Approach to Wave Field Synthesis: PBAP and Huygens Arrays'', by Julius O. Smith III, Published 2019-11-18:
Copyright © 2020-05-15 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University