Joint Source and Sensor Placement for Sound Field Control Based on Empirical Interpolation Method

Abstract

This study proposes a principled method to jointly determine the placement of acoustic sources (loudspeakers) and sensors (control points/microphones) in sound field control. The goal of this setup is to efficiently produce a sound field using multiple loudspeakers, approximately matching a target sound field over a region of interest. Therefore, the loudspeaker and control-point placement problem can be seen as the problem of finding interpolating functions (associated with individual loudspeaker sound fields) and sampling points (corresponding to control points or microphones) to approximate the target sound field in the given domain. We here solve this problem using the empirical interpolation method, originally developed for the numerical analysis of partial differential equations. The proposed method enables a joint determination of loudspeaker and control-point placement, from a large set of candidate locations, independently of the desired sound field. Numerical simulation results indicate that accurate and stable sound field control can be achieved by the proposed method, with significantly better results than with random and regular placements.