Regularized differentiation of measurement data using a priori information on signal and noise spectra

An algorithm previously proposed by the authors (see Proc. of Conf. EMISCON, Prague, 153-5, June 13-15, 1989) for real-time differentiation of discrete measurement data is further developed and studied. The effectiveness of this algorithm depends on a regularization parameter whose value should be fitted to the level of disturbances to which the data are subject. A simple method for choosing this value is proposed which requires only scanty a priori information on the data, namely an estimate of the signal bandwidth and an estimate of the signal-to-noise ratio. The effectiveness of this method is demonstrated using synthetic data and computer experimentation methodology. It is shown that the attainable accuracy of differentiation is very close to the optimum which may be reached by empirical optimization of the parameter of regularization