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. 1. Introduction In [1–4], electromagnetic responses, such as the driving-point current of an antenna, are simultaneously extrapolated in time and frequency by fitting discrete values of the response evaluated at early time and low-frequency points. Early-time and low-frequency data are mutually complementary and together can provide all the information needed to characterize the complete response [1–4]. Determining a wideband response of a resonant structure with computational electromagnetic (CEM) methods can be burdensome; however, extrapolation can significantly reduce the computational load since the complete response is not determined exclusively in either domain [1, 2]. An efficient and reliable procedure is presented here to extrapolate a response defined over an arbitrary spatial region, such as a contour, surface, or volume. As in [1, 2], the time and frequency behavior of the response is fitted by the sums of polynomials and pole terms. It is shown here that the spatial variation of a response can be accurately represented with sets of spatially-dependent coefficients for the polynomials and spatially-dependent residues for the pole terms. Additionally, it is demonstrated that a single set of
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