Sound field synthesis techniques aiming at the creation of virtual source sound fields, which are physically equivalent to the ones radiated by real sound sources. These techniques use an array of loudspeakers where an individual driving signal for each loudspeaker is determined according to a driving function. The synthesis of angle dependent radiation characteristics, as it is common for real sound sources, is a challenge for such reproduction systems. In this paper we present an approach for the synthesis of arbitrarily sound source radiation patterns using a planar array of loudspeakers. The method is based on the first Rayleigh integral formula and utilises an expansion of the virtual source sound field into spherical harmonics. Using this approach complex radiation patterns are conveniently presented by a set of expansion coefficients. Beside the derivation of the loudspeaker driving function, an analysis of its properties is performed. Numerical simulation results using a finite planar array of loudspeakers are also presented.
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