Wiener Filter Design Using Polynomial Equations
IEEE Transactions on Signal Processing,
vol 39, pp 2387-2399, November 1991. © 1991 IEEE.
Also: Internal Report UPTEC 90057R, Dept. of Technology,
Paper In Pdf (with figures) 1.0M.
Report, without figures, available in Postscript :
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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,
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 m-files
for polynomial equation design of Wiener estimators for scalar signals:
fnfilt.m Function for
abstar.m Used by fnfilt.m.
addcent.m Used by fnfilt.m.
spefac2.m Spectral factorization,
by polynomial roots, used by fnfilt.m
of Diophantine equation.
used by fnfilt.m
sylv.m Form sylvester matrix.
used by polysolve.m
- Related publications:
(Academic Press 1994), with additional aspects on the methodology.
Paper in IEEE Trans. AC 1993,
where the method is applied on LQG control
Paper in IEEE Trans AC 1995,
where method is used for deriving robust filters.
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