High-resolution radar becomes limited by the feeding mechanism in traveling wave antennas, forcing the design to some form of corporate feed. A spectral method of solving this problem is introduced which conveniently handles any transmitter pulse shape or receiver bandpass. The equivalence between this approach and an older transient solution is established. The method is applied to a uniform and a cosine illuminated aperture for both one- and two-way transmission through the antenna. It is shown that as a rule of thumb, the traveling wave feed should be less than half the spacial length of the transmitter pulse in the feed (

). Antennas exceeding this length must be divided into several sections, each of which must be corporately fed.