Numerical solution of the Wiener-Hopf equation in statistical identification of a linear dynamic plant. (Czech. English summary) Zbl 0171.17503

English summary: If a steady-state random input signal \(y\) acts on a linear dynamic plant, and if a steady-state noise, noncorrelated with the input signal, is superimposed on the output signal \(x\), it is possible to determine an unknown weight function of a plant \(h(x)\) by solving the Wiener-Hopf equation
\[ R_{yx}(\tau) = \int_0^\infty h(\vartheta) R_{yy}(\tau-\vartheta)\,d\vartheta, \quad \tau\geq 0, \]
where \(R_{yy}(\tau)\) is the auto-correlation function of the input signal, and \(R_{yx}(\tau)\) is the crosscorrelation function of the output and input signal of the plant. If the correlation functions are given graphically or tabularly, the above equation is solved numerically. Existing methods of solving this problem use an approximate substitution of a system of linear algebraic equations for the integral equation, the former being solved by finitary or iterative methods. This procedure presents some difficulties (badly conditioned system of linear equations, and the like). The authors propose therefore another approach to the solution of this problem. The new method of a numerical solution of the Wiener-Hopf equation described in this paper is based on a two-sided z-transform, and all numerical operations used therein have the character of a division of two polynomials.


94A12 Signal theory (characterization, reconstruction, filtering, etc.)
65R20 Numerical methods for integral equations
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