A new methodology is presented for characterizing an antenna system both in the time and frequency domain with one set of parameters using a singularity expansion method representation. A minimal set of parameter modeling antenna systems using the Matrix-Pencil method has been demonstrated. It has been shown that it is possible to obtain frequency-domain patterns from pole/residue models of antenna realized effective length. Thus, a pole/residue model of the antenna realized effective length presents a complete description in both the time and frequency domains. Once such a model is available, one can obtain the antenna pattern, directivity and gain in the frequency domain and the radiated transient waveform for an arbitrary excitation waveform and an arbitrary antenna orientation.