Soundfield reproduction using theoretical continuous loudspeaker

Reproduction of a soundfield is a fundamental problem in acoustic signal processing. A common approach is to use an array of loudspeakers to reproduce the desired field where the least square method is used to calculate the loudspeaker weights. However, the least square method involves matrix inversion which may lead to errors if the matrix is poorly conditioned. In this paper, we derive a new theoretical continuous loudspeaker method to obtain the loudspeaker aperture function in order to avoid matrix inversion. In addition, the aperture function obtained through continuous loudspeaker method reveals the underlying structure of the solution as a function of the desired soundfield, the loudspeaker positions and the frequency.