
Wiener Filter Design Using Polynomial Equations
Anders Ahlén
and
Mikael Sternad
IEEE Transactions on Signal Processing,
vol 39, pp 23872399, November 1991. © 1991 IEEE.
Also: Internal Report UPTEC 90057R, Dept. of Technology,
Uppsala University.
Paper In Pdf.
 Outline:

The classical concept of orthogonality is here utilized in
a novel way, within the polynomial equations approach
to linear filtering problems.
As a result, the process of deriving estimator design equations,
for a given problem and model structure in polynomial form,
is simplified
significantly.
 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.
 Matlab mfiles

for polynomial equation design of Wiener estimators for scalar signals:

fnfilt.m Function for
estimator design.
abstar.m Used by fnfilt.m.
addcent.m Used by fnfilt.m.
spefac2.m Spectral factorization,
by polynomial roots, used by fnfilt.m
polysolve.m Solution
of Diophantine equation.
used by fnfilt.m
sylv.m Form sylvester matrix.
used by polysolve.m
 Related publications:

Book chapter
(Academic Press 1994), with additional aspects on the methodology.
Paper in IEEE Trans. AC 1993,
where the method is applied on LQG control
problems.
Paper in IEEE Trans AC 1995,
where method is used for deriving robust filters.

Research
on polynomial methods

Main
entry in list of publications

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