Digital Differentiation Of Noisy Data Measured Through A Dynamic System

Design of discrete time differentiating filters, in presence of coloured noise and non--neglectable transducer dynamics is investigated. The signal and noise are described by ARMA--models, possibly with poles on jzj = 1. The MSE--optimal filter, based on a discrete time approximation of the derivative operator, is given by a spectral factorization and a linear polynomial equation. EDICS no. 4.3. Report UPTEC 90087R, Department of Technology, Uppsala University. Automatic Control and Systems Analysis Group, Department of Technology, Uppsala University, P O Box 27, S--751 03 Uppsala, Sweden. This work has partly been supported by the Swedish National Board of Technical Development, under contract 88--02549. 1 Introduction The problem of estimating derivatives of signals from noise corrupted measurements arises frequently. See, for example, [1]--[2]. Several design principles have been suggested, see [3]--[6] for some recent approaches. In [3] and [4], this problem was addressed by m..