On identification of nonstationary Hammerstein systems by the Fourier series regression estimate

A study is made of the identification of a single-input, single-output (SISO) discrete Hammerstein system. Such a system consists of a nonlinear, memoryless subsystem followed by a dynamic, linear subsystem. The authors identify the parameters of the dynamic, linear subsystem by the correlation method. The main results concern the identification of the nonlinear, memoryless subsystem. The authors impose no conditions on the functional form of the nonlinear subsystem, recovering the nonlinearity using the Fourier series regression estimate and an input process with fixed initial conditions. They prove the density-free pointwise convergence of the estimate, that is, that the algorithm converges for all input densities. The rates of pointwise convergence are obtained for smooth input densities and for nonlinearities of the Lipschitz type