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

Abstract

An algorithm for real-time differentiation of discrete measurement data is discussed. The effectiveness of this algorithm depends on a regularization parameter whose value should be fitted to the level of disturbance to which the data are subject. A simple method for choosing this value has been proposed and it 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 has been demonstrated using a few sets of synthetic data and computer experimentation methodology. It has been shown that the attainable accuracy of differentiation is very close to the optimum which may be reached via empirical optimization of the regularization parameter.<>