A number of methods have been proposed for the application of Wave Field Synthesis to the reproduction of sound fields generated by point sources that exhibit a directional radiation pattern. However, a straightforward implementation of these solutions involves a large number of real-time operations that may lead to very high computational load. This paper proposes a simplified method to synthesize virtual sources with axisymmetric radiation patterns using a planar loudspeaker array. The proposed simplification relies on the symmetry of the virtual source radiation pattern and on the far-field approximation, although also a near-field formula is derived. The mathematical derivation of the method is presented and numerical simulations validate the theoretical results.
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