Applying the Karhunen-Loève Expansion to Measurement of the Volterra Kernels

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  • Karhunen-Loève展開を応用したVolterra核の測定
  • Karhunen-Loeve展開を応用したVolterra核の測定
  • Karhunen Loeve テンカイ オ オウヨウシタ Volterra カ
  • Applying the Karhunen-Lo^|^egrave;ve Expansion to Measurement of the Volterra Kernels

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The measurement of the kernels of the Volterra series model of a nonlinear dynamical system is carried out as follows; first by applying orthogonal expansions to the kernels, a parametric model is derived, and then the parameters are optimally determined in the sense of the least mean square error over the whole length of the input-output observation of the system. In this general method, it is known that, if the test input is a white gaussian signal, a great saving is obtained in the amount of computation required to write the normal equation determining the optimal parameters. The purpose of the present paper is to show that, even when the test input is not white, by applying the Karhunen-Loève expansion to the input time series, it can be treated as if it is a white signel, and as the result, the same amount of computational saving as for the white gaussian input is obtained.

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