Best Linear Approximation of Wiener Systems Using Multilevel Signals: Theory and Experiments

The problem of measuring the best linear approximation of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by numerical simulations and by experiments on a practical circuit including an analog filter and a clipping nonlinearity. The performance of the sequences is compared with a white Gaussian noise signal for reference purposes. The theoretical characterization of the best linear approximation when using randomized constrained sequences is derived analytically for the cubic nonlinearity case. Numerical and experimental results show that the randomized constrained approach for designing ternary sequences has a low sensitivity to both even and odd order nonlinearities, resulting in a response close to the actual response of the underlying linear system.