Rendering of an Acoustic Beam through an Array of Loudspeakers

This paper addresses the problem of rendering a virtual source through loudspeaker arrays. The orientation of the virtual source and its aperture determine its radial beampattern. The methodology we present here imposes that the wavefield in a predetermined listening area best approximates the desired wavefield in the least squares sense. With respect to the traditional techniques the number of constraints is much higher than the number of loudspeakers. As a consequence, the loudspeaker coefficient vector is the solution of an over-determined equation system. Moreover this system may be ill-conditioned. In order to solve these issues, we resort to a least squares inversion combined with a Singular Value Decomposition (SVD) to attenuate the problem of ill-conditioning. Some experimental results show the feasibility and the issues of this methodology.