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Polynomial approach to Wiener filtering. (English) Zbl 0645.93062

The paper is concerned with the derivation of the multivariable Wiener filter using the polynomial approach. Both the discrete- and continuous- time case are treated in a mathematically rigorous way, using \(\Delta\)- transform and Laplace transform methods respectively. In particular it is shown that the approach described here involves one spectral factorization and the solution of one diophantine equation, while previously suggested polynomial methods for filtering and similar optimization problems required the solution of a pair of diophantine equations. Some simple scalar examples are finally examined.
Reviewer: G.Di Masi

MSC:

93E11 Filtering in stochastic control theory
11D99 Diophantine equations
44A10 Laplace transform
44A15 Special integral transforms (Legendre, Hilbert, etc.)
62M20 Inference from stochastic processes and prediction
93C55 Discrete-time control/observation systems
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References:

[1] DOI: 10.1080/0020718508961214 · Zbl 0573.93063
[2] KAILATH T., Linear Systems (1980)
[3] KUČERA V., Kybernetika 14 pp 110– (1978)
[4] DOI: 10.1093/imamci/3.4.311 · Zbl 0635.93018
[5] ROTH W. E., Proc. Am. math. Soc. 3 pp 392– (1952)
[6] WIENER N., Extrapolation, Interpolation and Smoothing of Stationary Time Series (1949) · Zbl 0036.09705
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