Spherical Harmonic Representation for Dynamic Sound-Field Measurements

Abstract

Continuously moving microphones produce a high number of spatially dense sound-field samples with low effort in hardware and acquisition time. By interpreting the dynamic procedure as the non-uniform sampling of spatial basis functions, a system of linear equations can be set up. Its solution encodes sound-field parameters that allow for the spatio-temporal reconstruction within the measurement area at bandwidths where static methods would require impractical setups. An existing framework considers such basis functions from a signal processing point of view. It uses sinc-function based interpolation filters which are highly localized around sampled trajectories and may lead to ill-posed problems unless sparsity constraints are made, especially for locations that are away from microphone trajectories. In this paper, we present a new physical interpretation of the dynamic sampling problem. Transferring the problem into frequency domain, we describe samples of a moving microphone in terms of sampled spherical harmonic functions. The use of these global basis functions leads to dynamic measurements that inherently encode expanded sound-field information and, thus, allow for robust reconstruction at off-trajectory positions.