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Recursive convolutions are believed to be the basic approach for digital calculation of electromagnetic transients on transmission systems. They require step responses expressed by means of exponential functions. This paper presents the theory for obtaining an arbitrary number of exponential components - with real or complex exponents directly from the frequency domain transfer function. The Inverse Fourier Transform is avoided by direct frequency domain fitting: either interpolation (exact for selected points) or weighted least squares approximation. Finally the method of recursive convolutions is generalized for complex exponentials.
A. Semlyen (1981) studied this question.