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The article presents a point of view for array-antenna analysis based on an operational calculus with two-dimensional Fourier transforms. The purpose is to describe the operational calculus, and to employ it in computing the array factor of a finite-extent phased array. Fourier-transform calculus is a very familiar subject to undergraduate electrical engineering students because of its central role in signal analysis, filter analysis and design, and in digital signal processing. The engineering control of the pattern through the parameters of the antenna configuration are particularly clear when the pattern is developed through a two-dimensional Fourier transform operational calculus.