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Rectangular reflector antennas have motivated the time-domain analysis of electromagnetic scattering problems. The asymptotic time domain physical-optics (TDPO) is applied to the analysis of a rectangular reflector illuminated by a Gaussian-impulse. The effects of time-delayed mutual coupling between points on the surface will be ignored as a result of utilizing the TDPO method for determining the equivalent surface-current density on the reflector. Finally, in this work the scattered signals at the specular reflection point, at the edges, and at the corners can be clearly distinguished.