Optimizing spherical loudspeaker array for voice directivity using the spherical cap model

Abstract

Conventional mouth simulators are limited by fixed radiation patterns, low power and high self-noise, failing to capture the complex spatial characteristics of real speech, such as the downward tilt of the main radiation lobe. To overcome these limitations, a simulation-driven approach is developed using the analytical spherical cap model, which was implemented and validated against known reference from the work of Aarts and Jansen [ 1 ]. This thesis investigates the optimization of a spherical loudspeaker array to accurately reproduce the dynamic and articulation-dependent directivity patterns of the human voice. A grid-search optimization method is applied to evaluate physical parameters, including array radius , driver radius , for different layouts (1, 4, 9, and 16 drivers), using a magnitude-weighted energy error metric. The single-driver configuration served as baseline proving the existence of optimal points, whereas they were found to be acoustically insufficient for replicating the asymmetric and time-varying nature of human speech. In contrast, by utilizing a frequency-dependent regularized least-squares control strategy (Tikhonov regularization) the multi-driver arrays successfully reproduce the higher-order spatial modes required to match measured phoneme patterns. The results indicate that a 16 driver configuration provides a critical threshold of perceptual authenticity, effectively reproducing the downward-tilted radiation lobes of vowels and the unique spatial signatures of fricatives and nasals. This work establishes a robust framework for developing physical prototypes.