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

TL;DR

This paper investigates methods for accurately approximating Wiener systems with multilevel signals, providing theoretical analysis and experimental validation, and demonstrating the effectiveness of randomized constrained sequences in capturing linear system responses.

Contribution

It introduces a theoretical framework for the best linear approximation of Wiener systems using multilevel signals and compares different sequences through simulations and experiments.

Findings

Randomized constrained sequences show low sensitivity to nonlinearities.

Ternary sequences closely approximate the linear system response.

Experimental results validate the theoretical analysis.

Abstract

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.