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Multiresolution Sampling Considerations

Intuitively, spatial sample reconstruction requires that each driver be capable of pressurizing a fraction of one wavelength (in its band) to the desired pressure level. Thus, while the speakers are ideally very small, on the order of drinking-straw diameters at high frequencies, the drivers need a long excursion in order to push enough air down the straw to achieve the desired pressure within the subwavelength zone being served. It is straightforward to calculate the maximum piston excursion needed for a given sound pressure level and lowest sinusoidal frequency. Dividing up the spectrum into frequency bands makes this easier.

The exact shape of the drivers is not important when they are smaller than a wavelength, only that they can pressurize their subwavelength zone as needed. Perhaps the easiest solution conceptually is a grid of contiguous square pistons. In that case it is easy to see that it must work very well, because the pistons can generate the wave propagation leaving the surface in great detail.

In classical ``critical sampling,'' there would two pistons per wavelength, one to push while the adjacent piston pulls. In practice, critical sampling may cause undesired noise due to turbulence, since there is no guarantee that laminar flow is maintained. Obtaining silent pressurization of half a wavelength may prove difficult at high sound pressure levels, so spatial oversampling helps.

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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