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A discrete convolution procedure is applied to the synthesis of radiation patterns with prescribed sidelobe levels. This procedure begins with a target polynomial, such as Chebyshev or Taylor, and determines the array element amplitudes by a simple, closed-form, noniterative computational method. Symmetrical hexagonal arrays of 3n2 + 3n + 1 elements, where n is the number of rings in the array, and symmetrical square arrys of (2m + 1)2 elements are analyzed. Examples are presented, and this procedure is compared with other synthesis methods.