Generation of a ultrawideband electromagnetic response through a Laguerre expansion using early time and low frequency data

The objective of this paper is to generate a ultrawideband and long temporal response for three-dimensional structures. This is accomplished through the use of a hybrid method that involves generation of early time and low frequency information for the electromagnetic structure of interest utilizing computational available conventional electromagnetic codes. These two, early time and low frequency information, are mutually complementary and contain all the necessary information for an ultrawideband response for a sufficient record length. The time domain response is modeled as a Laguerre series expansion. The frequency domain response is also expressed in an analytic form using the same expansion coefficients used in the modeling of the time domain response. The data in both the domains is used to solve for the polynomials coefficients in a data fitting procedure. Once the polynomial coefficients are known, the available data is simultaneously extrapolated in both domains. This approach is attractive because expansions with a few terms give good extrapolation in both the time and frequency domains. The computation involved to generate a ultrawideband response is minimal with this method.