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A method is presented whereby one can extract the singularity expansion method (SEM) description of an object's electromagnetic scattering response from spatially sampled transient surface currents. The currents are excited by a known excitation. The SEM data are recoverable to the degree that spatial coupling and (frequency) spectral intensity excite a given SEM mode. Results of a numerical study of the method using the transient response of a thin wire are reported. The data used in the study were computed using a time domain integral equation technique. The ultimate utility of the method lies in the recovery of SEM data from measured data, thus admitting complex-shaped objects into the realm of SEM description. The method is based on a Prony-type pole/residue extraction procedure.