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- Wiener_series abstract "In mathematics, the Wiener series (or Wiener G-functional expansion) originates from the 1958 book of Norbert Wiener. It is an orthogonal expansion for nonlinear functionals closely related to the Volterra series and having the same relation to it as an orthogonal Hermite polynomial expansion has to a power series. The analogue of the coefficients are referred to as Wiener kernels. The terms of the series are orthogonal (uncorrelated) with respect to a statistical input of white noise. This property allows the terms to be identified in applications by the Lee-Schetzen method.The Wiener series is important in nonlinear system identification. In this context, the series approximates the functional relation of the output to the entire history of system input at any time. The Wiener series has been applied mostly to the identification of biological systems, especially in neuroscience.The name Wiener series is almost exclusively used in system theory. In the mathematical literature it occurs as the Ito expansion (1951) which is entirely equivalent to it. (The Wiener series should not be confused with the Wiener filter, which is an unrelated concept.)".
- Wiener_series wikiPageID "27608024".
- Wiener_series wikiPageLength "4889".
- Wiener_series wikiPageOutDegree "13".
- Wiener_series wikiPageRevisionID "703913664".
- Wiener_series wikiPageWikiLink Category:Functional_analysis.
- Wiener_series wikiPageWikiLink Category:Mathematical_series.
- Wiener_series wikiPageWikiLink Functional_(mathematics).
- Wiener_series wikiPageWikiLink Neural_Computation_(journal).
- Wiener_series wikiPageWikiLink Norbert_Wiener.
- Wiener_series wikiPageWikiLink Science_(journal).
- Wiener_series wikiPageWikiLink Spike-triggered_average.
- Wiener_series wikiPageWikiLink System_identification.
- Wiener_series wikiPageWikiLink Volterra_series.
- Wiener_series wikiPageWikiLink White_noise.
- Wiener_series wikiPageWikiLink Wiener_filter.
- Wiener_series wikiPageWikiLinkText "Wiener kernel".
- Wiener_series wikiPageWikiLinkText "Wiener series".
- Wiener_series wikiPageUsesTemplate Template:Cite_book.
- Wiener_series wikiPageUsesTemplate Template:Cite_journal.
- Wiener_series subject Category:Functional_analysis.
- Wiener_series subject Category:Mathematical_series.
- Wiener_series type Function.
- Wiener_series comment "In mathematics, the Wiener series (or Wiener G-functional expansion) originates from the 1958 book of Norbert Wiener. It is an orthogonal expansion for nonlinear functionals closely related to the Volterra series and having the same relation to it as an orthogonal Hermite polynomial expansion has to a power series. The analogue of the coefficients are referred to as Wiener kernels. The terms of the series are orthogonal (uncorrelated) with respect to a statistical input of white noise.".
- Wiener_series label "Wiener series".
- Wiener_series sameAs Q4402522.
- Wiener_series sameAs m.0c3w_sd.
- Wiener_series sameAs Ряд_Винера.
- Wiener_series sameAs Q4402522.
- Wiener_series wasDerivedFrom Wiener_series?oldid=703913664.
- Wiener_series isPrimaryTopicOf Wiener_series.