Identification of the Nonlinear Element in Wiener Models A Frequency-Geometric Solution

We are considering the problem of identifying Wiener nonlinear systems. The focus is made on the determination of the underlying nonlinear element. This is allowed to be noninvertible and discontinuous while the linear dynamics are arbitrary but stable. A deterministic solution is designed using tools from differential geometry and frequency analysis. The solution necessitates a single frequency experience involving a sinus input with fixed amplitude and frequency. The obtained experimental data are used to build up a family of (memory) Lissajous curves. The nonlinear element is recovered from the only curve that present a static shape. The estimate thus obtained is shown to be unbiased in presence of any ergodic stationary noise