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Wrapped Polygonal PBAP (WPPBAP)

A problem with VBAP's sweet-spot size is that each speaker is approximately a spherical wave source. Therefore, Truncated Polygonal PBAP produces quasi spherical waves from each polygon side (when the wavelength is large compared with polygon side length). To address this, we can use nearly half of all speakers surviving the truncation to participate in the plane-wave generation from each original line array.

In particular, starting with Polygonal PBAP, the process of truncating to the interior polygon can include summing the signal ``seen'' from each truncated speaker arriving at each surviving speaker. This is essentially just applying the sampling principles used to derive PBAP in the first place. Thus, each speaker signal will include the signal from its original line array, plus a delayed and attenuated signal from each truncated speaker that is ``behind it'' relative to the listener, and reasonably close. The truncated speakers are now treated as point sources, so the attenuation is proportional to inverse-distance as usual for spherical waves. A maximum distance is set beyond which speakers from the (imagined) extended line array are not heard. This leaves less than half of the surviving speakers receiving contributions from the truncated speakers on any given line array.

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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