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The objective of this paper is to generate a wideband and temporal response of three-dimensional composite structures by using a hybrid method that involves generation of early time and low-frequency information. The data in these two separate time and frequency domains are mutually complementary and contain all the necessary information for a sufficient record length. Utilizing a set of orthogonal polynomials, the time domain signal (be it the electric or the magnetic currents or the near/far scattered electromagnetic field) could be expressed in an efficient way as well as the corresponding frequency domain responses. The available data is simultaneously extrapolated in both domains. Computational load for electromagnetic analysis in either domain, time or frequency, can be thus significantly reduced. Three orthogonal polynomial representations including Hermite polynomial, Laguerre function and Bessel function are used in this approach. However, the performance of this new method is sensitive to two important parameters-the scaling factor l/sub 1/ and the expansion order N. It is therefore important to find the optimal parameters to achieve the best performance. A comparison is presented to illustrate that for the classes of problems dealt with, the choice of the Laguerre polynomials has the best performance as illustrated by a typical scattering example from a dielectric hemisphere.