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).