Filter Design via Inner-Outer Factorization: Comments on
"Optimal Deconvolution Filter Design Based on
Signal Processing, vol 35, no 1, pp 51-58,
© 1994 Elsevier Science B.V.
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Stochastic model-based design of filters is often
based on the minimization of mean square estimation errors.
The paper discusses and compares several methods for deriving
this optimal solution.
In particular, it investigates the relation between methods based on
inner-outer factorization and other methodologies.
This paper is written with two purposes in mind.
First, it points out some mistakes made in
``Optimal deconvolution filter design
based on orthogonal principle'',
recently published in this journal.
Secondly, in order to sort out the reason for
those mistakes, the relations between
inner--outer factorization, spectral
factorization, whitening filters and
Diophantine equations in MMSE
filter design are stressed.
It is emphasized that computation of an
inner matrix corresponds to performing a
spectral factorization and the inverse of
the outer matrix is a whitening filter. Furthermore,
finding the causal part of an expression is
the same as solving a Diophantine equation.
- Related publications:
(Academic Press 1994) with further comparisons of derivation
in IEEE Trans. ASSP 1989 on the design of scalar deconvolution
in IEEE Trans. SP 1991 on multi-channel deconvolution.