In security relevant workspaces, such as air traffic control rooms, near field beam forming in small spaces is an important task. In this paper, a sound design based on a set of n-linear loudspeaker arrays where each consists of m-elliptic loudspeakers is investigated from a mathematical point of view. Based on these results, optimized array parameters are determined and useful approximations are developed. Three-Dimensional near field directional diagrams of the sound pressure in front of the arrays are shown to visualize the sound field. These diagrams are plotted and evaluated for different frequencies and distances of the field point, in addition to variations in the control signal phases and amplitudes. Finally, these theoretical values are compared with practical results.
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