An efficient procedure is presented to extrapolate a wideband electromagnetic response defined over an arbitrary spatial region using early-time and low-frequency data. The previous procedures presented in the literature are efficient for single-point extrapolation and can readily be applied to spatial regions but are terribly inefficient when a response is desired at many spatial locations. In this work, an optimized algorithm is presented to quickly extrapolate over a large number of spatial locations. The time and frequency behavior of the response is fitted by polynomials and pole terms, and the spatial variation is represented with spatially dependent polynomial coefficients and pole residues. A single set of poles, common to all spatial locations of interest, is shown to sufficiently describe the resonant behavior of response over the entire spatial region. A multisignal formulation of the matrix pencil method is applied to determine poles from early time data. Numerical examples are presented to demonstrate the procedure. Additionally, an automated approach to distinguish physical poles, which correspond to structural resonances, from nonphysical fitting poles is presented. The spatially dependent residues of physical pole terms, referred to here as modal residues, are shown to provide important insight into the resonant behavior of a structure.
Wideband Extrapolation of Spatial Responses of Resonant Structures Using Early-Time and Low-Frequency Data