Filter Design via Inner-Outer Factorization: Comments on "Optimal Deconvolution Filter Design Based on Orthogonal Principle"

Anders Ahlén and Mikael Sternad

Signal Processing, vol 35, no 1, pp 51-58, January 1994.
© 1994 Elsevier Science B.V.

Available in Pdf.

Outline:

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.

Abstract:

This paper is written with two purposes in mind. First, it points out some mistakes made in the paper ``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:

Book chapter (Academic Press 1994) with further comparisons of derivation methods.
Paper in IEEE Trans. ASSP 1989 on the design of scalar deconvolution estimators.
Paper in IEEE Trans. SP 1991 on multi-channel deconvolution.