Extrapolation of time and frequency responses of resonant antennas using damped sinusoids and orthogonal polynomials

An extrapolation technique is presented which reduces the computational demands of obtaining a wide-band electromagnetic response from a resonant antenna using traditional computational electromagnetic (CEM) methods. It has been shown that a wide-band response can be extrapolated by fitting early-time and low-frequency data as a finite summation of orthogonal polynomials. However, because the orthogonal polynomials provide compact time support, representation of the long time responses intrinsic to resonant structures in practice proves computationally inefficient and can lead to numerical instabilities. This paper outlines the incorporation of damped sinusoids to efficiently, accurately, and reliably extrapolate both time- and frequency-domain responses of resonant antennas due to a wide-band source. A genetic algorithm (GA) is used to select the necessary extrapolation parameters. The wide-band driving-point current response of several resonant antennas is accurately extrapolated. The transmission-line matrix (TLM) method and the method of moments (MoM) are used to compute early-time and low-frequency data, respectively. Fundamentally different discretizations of the structure of interest are used, illustrating in principle the independence of the technique and the choice of computational methods employed to provide the necessary input data.