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A singularity-expansion-method-based methodology is proposed for the accurate time- and frequency-domain analysis and modeling of wave radiation processes in ultrawideband antennas. By means of this approach, the transient electromagnetic field distribution in the Fraunhofer region is presented in analytical closed form as the superposition of outgoing propagating non-uniform spherical waves. The time dependence of the wave amplitudes is determined by the resonant phenomena occurring in the structure. Analytical expressions for the antenna gain and effective height are derived. The major novelties of the presented formulation lie in a dedicated two-step vector fitting procedure for a minimal pole/residue spherical harmonic expansion of the time-domain equivalent electric and magnetic currents excited on a suitable spherical Huygens surface enclosing the antenna under analysis, as well as in the introduction of a new class of incomplete spherical Bessel functions useful to describe transient wave phenomena in truncated structures. The proposed approach is validated by application to an ultrawideband resistively loaded bow-tie antenna for ground-penetrating radar applications.