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Non-linearity recovering with the help of wavelets

The non-linear characteristic of a system is recovered from noised observations. Three types of systems are considered: memoryless, Hammerstein and Wiener system. In Hammerstein system, the non-linear memoryless component is followed by a linear dynamics and in Wiener system the subsystems are connected in reverse order. The nonlinear characteristic is assumed to be square integrable and the input signal and disturbance are stationary white random processes. The non-linearity is recovered from input-output observations of the whole system. Identification algorithms are non-parametric and apply wavelet functions. Their pointwise convergence to the non-linear characteristic is shown.