Theory and design of soundfield reproduction using continuous loudspeaker concept

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-squares method is used to calculate the loudspeaker weights. However, the least-squares method involves matrix inversion which may lead to errors if the matrix is poorly conditioned. In this paper, we use the concept of theoretical continuous loudspeaker on a circle to derive the discrete loudspeaker aperture functions by avoiding 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. This concept can also be applied for the 3-D soundfield reproduction using spherical harmonics analysis with a spherical array. Results are verified through computer simulations.