Digital differentiation of noisy data measured through a dynamic system

The design of discrete time differentiating filters, in the presence of colored noise and nonneglectable transducer dynamics, is investigated. The signal and noise are described by autoregressive moving average (ARMA) models, possibly with poles on mod z mod =1. The mean square error (MSE) optimal filter, based on a discrete time approximation of the derivative operator, is given by a spectral factorization and a linear polynomial equation.<
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