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Results are demonstrated that show that for a given time-domain measurement of a relaxational system to given accuracy, it is possible to compute the equivalent frequency-domain response to comparable accuracy. The computation is well defined, numerically stable, and is independent of any assumed functional form. The error propagation is given by explicit analytical results that allow for experimental design for a given desired level of precision. For the numerical transformation of analytically defined functions, it provides an efficient numerical integrator with prescribed numerical accuracy.