Roberts, A. P.; Newmann, M. M. Polynomial approach to Wiener filtering. (English) Zbl 0645.93062 Int. J. Control 47, No. 3, 681-696 (1988). 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 Cited in 1 ReviewCited in 4 Documents 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 Keywords:multivariable Wiener filter; polynomial approach; spectral factorization; diophantine equation; continuous-time PDFBibTeX XMLCite \textit{A. P. Roberts} and \textit{M. M. Newmann}, Int. J. Control 47, No. 3, 681--696 (1988; Zbl 0645.93062) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.