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Increasing the Number of Source Angles

The number of available ray angles in PBAP can be increased by various means.

Oversampling in time to $ f_s=96$ kHz doubles the number of integer-delay angles over the same range. The example of Eq.(7) on page [*] goes from 21 to 41 angles-of-arrival across a $ 90^\circ$ frontal stage.

Another avenue for doubling the number of source angles is to implement a half-sample fractional-delay filter. In that case, half of the available angles require use of the filter while the other half require no interpolation filter.

Generalizing, given $ L-1$ fractional-delay filters, with the $ l$ th filter providing fractional delay $ l/L$ samples, $ l=1,2,\ldots,L-1$ , the number of available arrival angles is increased by the factor $ L$ . A benefit of a fixed grid of available angles is that each fractional-delay filter can be individually designed and optimized for the delay it provides. Three such filters ($ L=4$ ) suffice to provide approximately complete perceptual resolution in the example of Eq.(7).

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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