Fazi, Filippo Maria and Nelson, Philip A.
Sound field reproduction with an array of loudspeakers
Rivista Italiana di Acustica, 35, (1)
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The theory and the experimental realization are presented of a system for the reconstruction of a desired sound field within an array of loudspeakers. The array is modelled mathematically by means of an integral operator (single layer potential) and the loudspeaker input signals are obtained from the solution of an inverse system, more specifically an integral equation of the first kind. The solution of the problem is computed by means of the singular value decomposition of the integral operator, for which a physical interpretation is proposed, consistent with the engineering application in question. An analytical solution is calculated for the case of a spherical array. Finally, the experimental realization is described of a spherical array of 40 loudspeakers which was used for the reproduction of a target sound field generated by an omnidirectional source arranged in the exterior of the array. The target sound field and the reproduced field were measured with a microphone array and the results are compared for two operating frequencies. The paper aims at providing a contribution towards the development of a novel multi-channel signal processing strategy, which can be implemented in commercial 3D audio reproduction systems.
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