## Available Nonlinearity Estimators for Hammerstein-Wiener Models

System Identification Toolbox™ software provides several scalar nonlinearity estimators, for Hammerstein-Wiener models. The nonlinearity estimators are available for both the input and output nonlinearities f and h, respectively. For more information about f and h, see Structure of Hammerstein-Wiener Models.

Each nonlinearity estimator corresponds to an object class in this toolbox. When you estimate Hammerstein-Wiener models in the System Identification app, the toolbox creates and configures objects based on these classes. You can also create and configure nonlinearity estimators at the command line. For a detailed description of each estimator, see the references page of the corresponding nonlinearity class.

Piecewise linear
(default)
idPiecewiseLinearA piecewise linear function parameterized by breakpoint locations.By default, the number of breakpoints is 10.
One layer sigmoid networkidSigmoidNetwork

$g\left(x\right)=\sum _{k=1}^{n}{\alpha }_{k}\kappa \left({\beta }_{k}\left(x-{\gamma }_{k}\right)\right)$

$\kappa \left(s\right)$ is the sigmoid function $\kappa \left(s\right)={\left({e}^{s}+1\right)}^{-1}$. ${\beta }_{k}$ is a row vector such that ${\beta }_{k}\left(x-{\gamma }_{k}\right)$ is a scalar.

Default number of units n is 10.
Wavelet networkidWaveletNetwork

$g\left(x\right)=\sum _{k=1}^{n}{\alpha }_{k}\kappa \left({\beta }_{k}\left(x-{\gamma }_{k}\right)\right)$

where $\kappa \left(s\right)$ is the wavelet function.

By default, the estimation algorithm determines the number of units n automatically.
SaturationidSaturationParameterize hard limits on the signal value as upper and lower saturation limits.Use to model known saturation effects on signal amplitudes.
One-
dimensional polynomial
idPolynomial1DSingle-variable polynomial of a degree that you specify.By default, the polynomial degree is 1.
Unit gainidUnitGain

Excludes the input or output nonlinearity from the model structure to achieve a Wiener or Hammerstein configuration, respectively.

Note

Excluding both the input and output nonlinearities reduces the Hammerstein-Wiener structure to a linear transfer function.

Useful for configuring multi-input, multi-output (MIMO) models to exclude nonlinearities from specific input and output channels.

Custom network

(user-defined)

idCustomNetwork

Similar to sigmoid network but you specify $\kappa \left(s\right)$.