Spherical harmonic decomposition of a sound field based on observations along the equator of a rigid spherical scatterer
Jens Ahrens, Hannes Helmholz, David Lou Alon, Sebastià V. Amengual Garí
Abstract
We present a method for computing a spherical harmonic representation of a sound field based on observations of the sound pressure along the equator of a rigid spherical scatterer. Our proposed solution assumes that the captured sound field is height invariant so that it can be represented by a two-dimensional (2D) plane wave decomposition (PWD). The 2D PWD is embedded in a three-dimensional representation of the sound field, which allows for perfectly undoing the effect of the spherical scattering object. If the assumption of height invariance is fulfilled, then the proposed solution is at least as accurate as a conventional spherical microphone array of the same spherical harmonic order, which requires a multiple of the number of sensors. Our targeted application is binaural rendering of the captured sound field. We demonstrate by analyzing the binaural output signals that violations of the assumptions that the solution is based on-particularly height invariance and consequently also horizontal propagation-lead to errors of moderate magnitude.