Initial estimates for Wiener-Hammerstein dynamics using phase-coupled multisines

Even if nonlinear distortions are often present, many dynamical systems can be approximated by a linear model. When the nonlinear distortions are too large, however, a linear model is insufficient, and a nonlinear model is needed. One possibility is to use block-oriented models. These models consist of linear dynamic (L) and nonlinear static (N) sub-blocks. We propose a simple initialization method for a Wiener-Hammerstein model (LNL cascade). The product of the transfer functions of the two linear blocks can be easily obtained via the best linear approximation (BLA) of the system for a Gaussian excitation. Splitting the global dynamics over the individual blocks turns out to be more difficult. We propose a well-designed multisine excitation and a modified BLA on a shifted frequency grid. The input dynamics are shown to shift with a frequency offset that can be chosen by the user, while the output dynamics do not shift. This allows us to separate the two linear blocks via a simple initialization method, based on a linear system identification step. Experimental results obtained from the Wiener-Hammerstein benchmark system illustrate the good performance of the method.