This paper addresses the problem of Wiener system identification. The underlying linear subsystem is stable but not necessarily parametric. The nonlinear element in turn is allowed to be nonparametric, noninvertible, and nonsmooth. As Wiener models are uniquely defined up to an uncertain multiplicative factor, it makes sense to start the frequency identification process estimating the system phase (which is common to all models). To this end, a consistent estimator is designed using analytic geometry tools. Accordingly, the system frequency behavior is characterized by a family of Lissajous curves. Interestingly, all these curves are candidates to modelling the system nonlinearity, but the most convenient one is the less spread of them. Finally, the frequency gain is in turn consistently estimated optimizing an appropriate cost function involving the obtained phase and nonlinearity estimates.

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