Optimal deconvolution based on polynomial methods

The problem of estimating the input to a known linear system is treated in a shift operator polynomial formulation. The mean-square estimation error is minimized. The input and a colored measurement noise are described by independent ARMA (autoregressive moving average) processes. The filter is calculated by performing a spectral factorization and solving a polynomial equation. The approach can be applied to input prediction, filtering, and smoothing problems as well as to the use of prefilters in the quadratic criterion. It applies to nonminimum-phase as well as unstable systems, as illustrated by two examples.<
>