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Since the introduction of the singularity expansion method (SEM) for the representation of transient and broadband electromagnetic interaction with general objects, there has been considerable attention given to associated analysis of electromagnetic response experimental data to find the natural frequencies. Usually, this has considered only single waveforms of frequency spectra for a parameter such as the surface current density at a particular position on the object under some particular excitation such as a particular direction of incidence with a particular polarization. This paper explores several concepts for advancing the analysis of interaction data to obtain the various SEM and eigenmode expansion method parameters. Basically, the various properties of natural modes and eigenmodes are explored for application to the problem of the taking and analyzing of experimental data. Various techniques are explored, including the enforcement of the SEM pole factors in multiple data records, separation of the modes by object symmetry, separation of the modes into E and H modes by measurement of surface charge density and equivalent magnetic charge density, and separation of the natural modes and natural frequencies by association with eigenmodes and use of eigenmode orthogonality. Basically, these concepts involve application of a priori physics to the design of experiments and data analysis.