Scientific Article

Diffuse sound field synthesis: Towards practical source layouts

Institute of Electronic Music and Acoustics, University of Music and Performing Arts, 8010 Graz, Austria

^* Corresponding author: zotter@iem.at

Received: 11 October 2024
Accepted: 22 April 2025

Abstract

In an ideal isotropic diffuse sound field, uncorrelated plane waves arrive uniformly from all directions. Recent theoretical work has shown that uncorrelated sources arranged on a spherical surface can also be used to synthesize diffuse fields that exhibit a uniformly vanishing active sound intensity, albeit without position-independent isotropy. How the principles extend to finite-sized rectangular cuboid and discrete source layouts remains an open question. This study considers the multi-axial superellipsoid as a flexible parametric geometry for uncorrelated acoustic source distributions. By tuning its shape parameter p, the superellipsoid transitions from an ellipsoid p=2 to a rectangular cuboid p→∞, enabling a systematic analysis of active intensity using differential geometry, Gegenbauer expansion, and numerical simulations. Findings indicate that a superellipsoidal source layer of directionally uniform density requires to be driven by a non-uniform source variance, for which a generic solution is proposed. For the ellipsoid, the proposed variance is exact and emphasizes distant sources, while for the rectangular cuboid, it remains an approximation, but still effectively emphasizes sources near edges and corners. For discrete source layouts, zero active intensity can be approximately synthesized within a domain shrunk by a factor of N/(N+1) provided that (i) sources are arranged in uniform directions of a tight spherical 2N+1 design and sample the proposed variance, or (ii) a comparable number of sources with uniform variance is distributed in a minimum potential energy configuration.