Nonlinear dynamics and noise cancellation

The use of linear and nonlinear prediction in forming the inverse of a linear system is explored. The topic is introduced from the perspective of communications channel equalisers, where the signal of interest is stochastic, and from the perspective of nonlinear noise cancelling, where the signal of interest may be deterministic and chaotic. In both applications a nonlinear inverse to a linear system can produce better results than a linear inverse. The nonlinear architectures considered are linear-in-the-parameter radial basis function (RBF) and Volterra series (VS) networks. The application of nonlinear filtering techniques to the cancellation of noise in a linear duct is also considered. It is demonstrated that the required inverse is provided by the parallel connection of a linear and nonlinear network of different memory lengths