Criterion for the performance analysis of synchronous and asynchronous sampling instruments based on nonlinear processing

The authors 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, RMS 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. The particular formulae for different sampling strategies and filtering algorithms are discussed and compared.