The fundamental basis of the analysis presented in this section appears in [2], [3], [4], [7], [8], [9], [12], [13], [14], [15], and [16]. Here we extend these results to accommodate multiple, electronically-steered arrays consisting of elements possessing frequency-dependent amplitude, phase, and polar directivity characteristics. Also shown is how the array ensemble directivity pattern is mapped onto the "ear plane" of an audience scaling area. The resulting mathematical model is incorporated into a computer-aided design tool, described in Section 2 of this paper.
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