For the first-time to the authorspsila knowledge, pulse radiation by a LWA antenna has been characterized, using a novel time-domain Greenpsilas function approach. This characterization has been performed for both a CRLH LWA element and for a CRLH LWA array in the case of a Gaussian pulse modulated by a CW and by a chirp. In the former case, spectrograms have been computed and shown to be in perfect agreement with full-wave FDTD results. In the latter case, instantaneous beam motion under chirp-modulated pulse excitation has been described with possible application to instantaneous radar scanning. In all cases, the proposed method is extremely flexible and fast, because the time dependence of the fields is intrinsically contained in the Greenpsilas function and does not suffer of any restriction such as typical stability conditions in completely numerical time-domain methods.