Dynamic Uncertainty for Compensated Second-Order Systems

The compensation of LTI systems and the evaluation of the according uncertainty is of growing interest in metrology. Uncertainty evaluation in metrology ought to follow specific guidelines, and recently two corresponding uncertainty evaluation schemes have been proposed for FIR and IIR filtering. We employ these schemes to compare an FIR and an IIR approach for compensating a second-order LTI system which has relevance in metrology. Our results suggest that the FIR approach is superior in the sense that it yields significantly smaller uncertainties when real-time evaluation of uncertainties is desired

Filtering, smoothing, and prediction using a control-loop spectral factorization method for coloured noise

A method for the linear least-squares estimation of random signals contaminated with random noise is shown that uses a new method of spectral factorization. It is shown that the optimal filter can be written entirely in terms of the two spectral factors of signal plus noise and noise-alone, and can be applied to the general case of coloured and white additive noise. The method of spectral factorization used is novel and uses control-system methodology

Wiener Filter Design Using Polynomial Equations

A simplified way of deriving of realizable and explicit Wiener filters is presented. Discrete time problems are discussed, in a polynomial equation framework. Optimal filters, predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations. A new tool for obtaining these equations, for a given problem structure, is described. It is based on evaluation of orthogonality in the frequency domain, by means of cancelling stable poles with zeros. Comparisons are made to previously known derivation methodology such as "completing the squares" for the polynomial systems approach and the classical Wiener solution. The simplicity of the proposed derivation method is particularly evident in multisignal filtering problems. To illustrate, two examples are discussed: a filtering and a generalized deconvolution problem. A new solvability condition for linear polynomial equations appearing in scalar problems is also presented. EDICS no. 4.2.2. Keywords: Wiene..