Optimal Deconvolution based on Polynomial Methods
IEEE Transactions on Acoustics, Speech and Signal
pp 217-226, February 1989. © 1989 IEEE.
Paper available in PDF (718k)
Deconvolution, or input estimation, is intricate for at least
two reasons: measurements are usually noise corrupted
and the system is frequently nonminimum phase.
These properties restrict the use of the simplest
deconvolution filter, namely the inverse system.
The paper discussed a systematic Wiener design of
deconvolution estimators which utilizes polynomial
The problem of estimating the input to a known linear
system is treated in a shift operator polynomial formulation.
The mean square estimation error is to be minimized.
The input and a colored measurement noise are described
by independent ARMA processes.
The filter is calculated by performing a spectral
factorization and solving a polynomial equation.
The approach covers input prediction, filtering and
and the use of prefilters in the quadratic criterion.
It is applicable to nonminimum phase as well as unstable systems.
This is illustrated by two examples.
The possible applications range from seismic signal processing
and linear MMSE equalization
to numerical differentiation of noisy signals.
- Matlab m-files
for polynomial equation design of scalar IIR
Wiener deconvolution estimators:
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
- Related publications:
Conference paper in SPIE'91
deconvolution based on spectral decomposition.
Paper in IEEE Trans. SP 1991
on differentiation of noisy data.
Paper in IJC 1993
on the duality between deconvolution and feedforward control.
Paper in Automatica 1993,
which includes robust
design based on averaged MSE criteria.
Paper in IEEE Trans. AC 1995,
which discussed robust design
of multivariable estimators.
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