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- W1974970084 abstract "A functional Fourier series is developed with emphasis on applications to the nonlinear systems analysis. In analogy to Fourier coefficients, Fourier kernels are introduced and can be determined through a cross correlation between the output and the orthogonal basis function of the stochastic input. This applies for the class of strict-sense stationary white inputs, except for a singularity problem incurred with inputs distributed at quantized levels. The input may be correlated if it is zero-mean Gaussian. The Wiener expansion is treated as an example corresponding to the white Gaussian input and this modifies the Lee-Schetzen algorithm for Wiener kernel estimation conceptually and computationally. The Poisson-distributed white input is dealt with as another example. Possible links between the Fourier and Volterra series expansions are investigated. A mutual relationship between the Wiener and Volterra kernels is presented for a subclass of analytic nonlinear systems. Connections to the Cameron-Martin expansion are examined as well The analysis suggests precautions in the interpretation of Wiener kernel data from white-noise identification experiments." @default.
- W1974970084 created "2016-06-24" @default.
- W1974970084 creator A5023020166 @default.
- W1974970084 date "1979-04-01" @default.
- W1974970084 modified "2023-10-17" @default.
- W1974970084 title "Stochastic functional fourier series, Volterra series, and nonlinear systems analysis" @default.
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- W1974970084 doi "https://doi.org/10.1109/tac.1979.1101990" @default.
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