A Spherical-Harmonic-Based Framework for Spatial Sampling Considerations of Musical Instrument and Voice Directivity Measurements

Abstract

Researchers have employed numerous array configurations and sampling densities to thoroughly measure the sound radiations of live sources, such as musical instruments and speech. The number of sampling positions has varied from fewer than a hundred to over a thousand, with measurement inconsistencies highlighting a knowledge gap in the number of sampling positions required for spherical directivity measurements. This work presents theoretical methods and practical metrics to assess the required number of sampling positions for a given source to mitigate spatial aliasing. Theoretical developments show that the number of necessary sampling positions closely relates to source geometry due to the spatial filtering effects of far-field propagation. Initial results from theoretical models generalize the approach to live sources.