Volterra-Tauberian estimation for nonlinear system identification

The theoretical aspects and mathematical framework of the time-invariant (TIV) nonlinear (weakly) system transfer function estimation and identification are considered to determine their feasibility. A mathematical framework is laid out in terms of the Volterra series. The approach attempts to circumvent conventional problems in identifying the nonlinear set of parameters that renders the Volterra series attractive to nonlinear systems but awkward to apply. Since an unknown TIV system is presumed for an observed output of some known input, measures applied for system linearity provide a means for identifying the existence of a nonlinear system. The methodology outlined provides an estimate of nonlinear system parameters that is useful in unknown communication channels which can be categorized by their particular nonlinear characteristic outputs. Such an approach facilitates identification of linear versus nonlinear channels, including differentiation between those identified as being nonlinear.<>