An Analytical Approach to Sound Field Reproduction Using Circular and Spherical Loudspeaker Distributions

In this paper, we present the theoretical basics and implementation strategies for sound field reproduction using circular and spherical loudspeaker arrays. The presented approach can be seen as an analytical formulation of what is known as higher order Ambisonics. It relies on the assumption of a continuous distribution of secondary sources on which sampling is performed to yield the loudspeaker driving signals for real-world implementations. We present the theoretical derivation of the loudspeaker driving signals and investigate the properties of the actual reproduced wave field, whereby the focus lies on the consequences of the spatial discretization of the secondary source distribution.