A singularity-expansion-method (SEM) based approach is presented for the analysis of radiation processes in short-pulse antennas. Any time-domain electromagnetic field solver can be used to derive a minimal pole/residue spherical harmonic expansion of the equivalent currents excited on a suitable Huygens surface enclosing the radiating structure. In this way, the time-domain effective height of the antenna is evaluated in closed form as the superposition of non-uniform spherical wave contributions attenuating along with the time according to the real part of complex poles accounting for the natural resonant processes occurring in the structure under analysis.