For reproducing a desired sound field from virtual sources, Wave Field Synthesis (WFS) assumes that virtual sources are positioned at far-field from the loudspeaker array. This far-field assumption inevitably produces reproduction errors when the virtual source is adjacent to the array. In this paper, we propose a method that can render the sound field from virtual sources positioned near the loudspeaker array. The driving functions of loudspeakers are derived for the planar array geometry, and then the surface integral is reduced to a line integral by utilizing different approximations from WFS. In addition, a modified equation for the discrete loudspeaker distribution is presented. Numerical simulations show that the proposed method can reduce the reproduction error to a practically acceptable level.
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