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 3D soundfield reproduction using spherical harmonics analysis with a spherical array. Results are verified through computer simulations.

Spatial multizone soundfield reproduction is a difficult problem, which has many potential applications. This paper provides a framework to recreate 2D spatial multizone soundfields using an array of loudspeakers. We derive the desired global soundfield by translating individual desired soundfields to a single global co-ordinate system and applying appropriate angular window functions. We reveal some of the fundamental limits of 2D multizone soundfield reproduction. We show that the ability of multizone reproduction is dependent on (i) maximum radius of multizones, (ii) window length (size, and nature), and (iii) radial distance to the furthermost zone. We illustrate the framework by designing and simulating a two dimensional two zone soundfield.

Any attempt to create multiple independent soundfields in separate zones over an extended region of open space results in unintended interference in a given zones from other zones. In this paper, we design spatial band stop filters to suppress interzone interference in the regions of interests and pass the desired soundfields with no distortion. This is achieved by using the higher order spatial harmonics of one zone to cancel the undesirable effects of the lower order harmonics of the same zone on the other zones. We illustrate the work by designing and simulating a 2D two-zone soundfield.Index Terms-soundfield reproduction, multizone, cylindrical harmonic expansions, spatial band stop filters.

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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. Results are verified through simulations.Index Terms-acoustic field, least square method, matrix inversion