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Size of the Accurate-Reproduction Area as Function of Directional Metrics in Spherical Harmonic Domain

In spherical harmonic sound field synthesis, spatial discretization of the sphere and truncation order decrease the physical performance in terms of acoustical pressure reproduction error. A simple rule allows for the prediction of the listening area’s size so that the deviation between the target and reconstructed sound pressure fields stays below a given level. However, this rule does not quantify the area of effective reproduction in terms of directional fields such as particle velocity or acoustical intensity. In this paper, a new rule for the effective reconstruction of particle velocity, acoustic intensity and, related directional metrics is derived and is found to be more severe than the usual pressure reconstruction. Numerical simulations of the directional fields and metrics are reported.

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