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This paper evolved from 2011 to now as a back-burner interest by the author who has never published previously in the field of spatial audio, and who has limited experience in the field, but much experience with bandlimited sampling theory. This paper contains the author's accumulated reactions to drilling down on currently used spatial audio methods such as Wave Field Synthesis (WFS) and Vector-Base Amplitude Panning (VBAP), without the level of background research (i.e., reading all known relevant papers) expected of a typical graduate student in the field. As a result, it is possible and even likely that some or many of the speaker arrays ``introduced'' here exist already in the literature and/or patent record in some form. The author welcomes citations that can be incorporated into an updated version of this paper.

Another result of the evolving nature of this paper is that it unfolds progressively from basic soundfield sampling to PBAP and its variations and finally to Huygens Arrays (HA). While it could make sense to write a fresh, shorter paper on one or more of these subtopics, the full story has greater tutorial value, and is less work to write, so here it all is in one relatively long paper.

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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