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- W2073598931 abstract "The <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2r</tex> th mean convergence of an adaptive filtering algorithm <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>C_{n+ 1} = C_{n} - a_{n}(C_{n}^{T} X_{n} - alpha_{n}) X_{n}</tex> is studied, where <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>alpha_{n}</tex> 's and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>X_{n}</tex> 's are useful random signals and observation vectors, respectively, and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>{ a_{n} }</tex> is a sequence of positive numbers decreasing to zero. In this work, we suppose that the sequence <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>{(alpha_{n},X_{n})}</tex> is a stationary mixing sequence ( <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>rho</tex> -mixing, <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>phi</tex> -mixing, or <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>psi</tex> -mixing). Under some additional conditions it is shown that <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>C_{n}</tex> converges to <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>c_{ast}</tex> in the <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2r</tex> th mean, where <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>c_{ast}</tex> is the unique solution of the Wiener-Hopf equation." @default.
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- W2073598931 date "1984-03-01" @default.
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- W2073598931 title "The<tex>2r</tex>th mean convergence of adaptive filters with stationary dependent random variables" @default.
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- W2073598931 doi "https://doi.org/10.1109/tit.1984.1056893" @default.
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