Wiener Filter Design Using Polynomial Equations

Abstract

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..