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Frequency-domain principle of pattern multiplication for array-fed reflector or lens antennas

In this letter, array-fed reflector or lens antennas are proven by using Fourier analysis methods to follow a kind of frequency-domain principle of pattern multiplication, which states that the spectrum of the composite field of such an antenna is the product of the spectrum of the far field of the individual spot beam and that of the excitation coefficient sequence. This principle will provide a useful and efficient tool not only for determining the optimum excitations but also for predicting the antenna performance.