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A new reflection and transmission analysis of a finite size frequency selective subreflector (FSS) due to a finite source located in the proximity of the FSS is presented. The field due to the finite source (in this case a corrugated feed horn) is first expanded in terms of the spectrum of the plane waves, and then, by employing the reflection and transmission matrices of the FSS the physical optics currents on a surface enclosing the FSS are constructed. From the currents and employing the field equivalence principle, the transmitted and reflected fields (scattered field) are found. The analysis presented is of importance to the design of advanced communication satellite antennas, where the FSS provides the multifrequency capabilities for the shaped reflector.