4 - Wiener Series

Abstract

This chapter discusses differences between the Wiener and Volterra series, which is helpful to derive the expressions for the zero-, first-, and second-order Wiener kernels. This chapter also discusses practical methods for determining Wiener kernels for simulated and recorded time series. Similar to the Volterra series, the Wiener series characterizes the output of a nonlinear system as the sum of a set of operators dependent on kernels and input. This equation is similar to the ones for the Volterra series, and, although there are many similarities between Volterra and Wiener series, there are also a few crucial differences that allow Wiener operators to be mutually independent. The first major difference is that a Volterra series usually does not include a zero-order term. The second major difference is that individual Volterra operators are homogeneous. The third and final major difference is that in the case of a Wiener series, one uses a special input signal, usually in the form of zero mean Gaussian white noise. Applications of these methods are used in the form of MATLAB scripts. This chapter summarizes the mathematical procedures that used to determine the Wiener series.