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Point-source frequency-response overlap-add magnitude for a 6 m array, with half-wavelength source spacing ( $ \approx 17$ cm), observed from a 12 m listening-line one wavelength away.

Figure: No array taper, showing much Gibbs oscillation due to array truncation.
\resizebox{0.9\textwidth }{!}{\includegraphics{eps/pointSourceFRSliceOLA35Taper0zlf1.eps}}

Figure: Sinusoidally tapered array edges over three wavelengths on each side.
\resizebox{0.9\textwidth }{!}{\includegraphics{eps/pointSourceFRSliceOLA35Taper3zlf1.eps}}

While spherical waves do not give perfect-reconstruction at half-wavelength overlap-add, one wavelength out, we see from the dB plots in Fig.19 that the error is quite small in audio terms. The ``ripple'' stays small down to well under wavelength $ z_l<\lambda$ before source proximity effects increase the ripple significantly. Note, incidentally, that we are ignoring the reactive ``mass'' component of the point-source field near its center, which is non-propagating (Morse and Ingard, 1968).

The ripple reduces as we get farther out from the array ( $ z_l>\lambda$ ) because the interpolation kernels expand, giving more overlap. (Increase the number of sources by the same factor to see this more clearly without additional array-truncation error.) Since we normally listen to arrays at some distance away, we see that a larger issue than sampling density is array extent; looking in the direction a wave is coming from, we should see plenty of samples surrounding the point that our ``look direction'' intersects along the array. The commonly used surrounding ring/sphere architectures (often set up for ambisonics or VBAP) are excellent in this respect: Every look direction has samples uniformly about/around it. Linear/planar arrays are at a disadvantage because they must be truncated or windowed, limiting the virtual stage view.

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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