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Undersampled Huygens Arrays become VBAP

A practical issue that arises when an array is allowed to undersample the soundfield is level normalization. An extreme example is the amplitude ($ \infty$ ) of a point source when it touches a microphone/speaker point on the array, which is well out of bounds for any reasonable practical system.

Level regularization is another reason to keep sources a few wavelengths or more away from the microphone/speaker array.

When the array becomes undersampled, say because a wideband source is approaching an extreme stage angle, the array can be regarded as transitioning from soundfield reconstruction by summing interpolation kernels to simple panning between/among available speakers (i.e., what we're normally always doing). Note that the high-frequencies must go into ``panning mode'' first, while lower frequencies may remain adequately sampled. We can implement an adaptive spectral partition between sample-based reconstruction below and panning above.21

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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