The utility of the array pattern matrix for linear array computations

Abstract
Operations with a class of matrices called pattern matrices represent essentially every step in the numerical calculation of the patterns of linear arrays. These matrices are especially suitable for use with high speed computers. The inverses of pattern matrices always exist so that they can be used for purposes of array pattern synthesis via Lagrangian interpolation. Securing a good fit to the specified pattern would call for many radiators, thus requiring the inversion of a matrix of high order. Consequently, a class of uniform pattern matrices is defined whose inversion can be accomplished by inspection, which is sufficiently general to be useful for most practical problems of interest. Uniform pattern matrices generate the coefficients of the Fourier expansion of the specified pattern and can be used, therefore, to help minimize the integral of the square of the deviation of the synthesized and specified patterns as functions of the phase variable,\psi.

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