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A two-period array of subwavelength holes in a perfect electrically conducting plate permits enhanced transmission of incident plane waves with wavenumbers near those of leaky waves supported by the array. A simple periodic impedance sheet model explains this phenomenon and provides an approximate expression for the transmission peak location. Transmission through thin perforated plates is studied using a full-wave solver to verify model-theoretic observations. Transmission coefficient peak splitting and narrowing phenomena, associated with thick perforated plates, are explored.