Abstract-This paper describes a modeling approach for nonlinear dynamic systems based on a modified Volterra series; by comparing the truncation error of this series with that of the classical Volterra one, we outlined that, under the assumption of short-term nonlinear memory effects, the modified series enables a single-fold nonlinear convolution integral to be adopted also in the presence of strong nonlinearities. The measurement-based identification of the first terms of the modified Volterra series is described; experimental and simulation results which confirm the theoretical considerations are also provided.

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We propose a criterion for the comparison of different sampling strategies (synchronous, asynchronous and random) and filtering algorithms used in digital instruments which provide the estimate of the time average of a signal processed with a nonlinear conversion of multiple inputs (e.g. wattmeters, R M S voltmeters, . . .). This criterion uses the Bayesian approach to incorporate, for every sampling strategy, any prior information on the influences of each incidental quantity which can vary the output of the instrument, transforming this output into a statistic. The asymptotic mean-squared error of the measurements has been assumed as an estimator of the error and its general expression, valid for the most common sampling strategies used in practice, has been deduced. This asymptotic error is a function of the frequency response of the digital filter used and, eventually, of the characteristic function of the probability distribution selected for the random variables generating the sampling instants. Finally, the particular formulae for different sampling strategies and filtering algorithms are discussed and compared.

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