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A new technique is presented here which utilizes both orthogonal polynomials and damped sinusoids to extrapolate time and frequency responses using only early-time and low-frequency data. Damped sinusoids are used to efficiently represent the effects of resonances while the remaining behavior is accurately characterized by polynomials. To ensure reliably accurate results, a genetic algorithm (GA) is used to select expansion parameters. The technique is demonstrated by extrapolating the driving-point current response of a resonant antenna.