Localizing Acoustic Energy in Sound Field Synthesis by Directionally Weighted Exterior Radiation Suppression

TL;DR

This work tackles the challenge of exterior radiation in sound field synthesis by introducing directionally weighted exterior radiation suppression, which prioritizes suppression in specific outward directions using a weight function $w(\theta,\phi)$. The exterior penalty is reformulated as a quadratic form $\bm{d}^{\mathsf{H}}\bm{A}\bm{d}$ via spherical-harmonic expansions, Gaunt coefficients, and translation operators, enabling seamless integration with existing synthesis methods. In particular, the authors apply this to amplitude matching, formulating a cost that combines interior synthesis error with the directionally weighted exterior term and a regularizer, and solving it with ADMM due to nonconvexity. Numerical experiments with 24 loudspeakers demonstrate substantial exterior-radiation reduction in prioritized directions while maintaining interior amplitude accuracy, highlighting the method’s practical potential for localized sound-field control in personal audio systems and AR/VR applications.

Abstract

A method for synthesizing the desired sound field while suppressing the exterior radiation power with directional weighting is proposed. The exterior radiation from the loudspeakers in sound field synthesis systems can be problematic in practical situations. Although several methods to suppress the exterior radiation have been proposed, suppression in all outward directions is generally difficult, especially when the number of loudspeakers is not sufficiently large. We propose the directionally weighted exterior radiation representation to prioritize the suppression directions by incorporating it into the optimization problem of sound field synthesis. By using the proposed representation, the exterior radiation in the prioritized directions can be significantly reduced while maintaining high interior synthesis accuracy, owing to the relaxed constraint on the exterior radiation. Its performance is evaluated with the application of the proposed representation to amplitude matching in numerical experiments.

Figures (6)

• Figure 1: Sound field synthesis using multiple secondary sources.
• Figure 2: Experimental setup. Blue dots and green cylinder represent loudspeakers and target region $\Omega$, respectively.
• Figure 3: MSE of AM, AM-Rad, and AM-Rad-Dir with respect to frequency.
• Figure 4: $P_{\mathrm{rad}}$ of AM, AM-Rad, and AM-Rad-Dir with respect to frequency.
• Figure 5: Power distribution of synthesized sound field on $x$-$y$-plane at $z=0$.