Recursive controllers for nonlinear active noise control

In this paper, we refer to the class of recursive linear-in-parameters nonlinear filters, i.e., the filters whose output depends linearly on their coefficients. In particular, we consider and compare the implementations and performance of three members of the class, i.e., recursive functional link artificial neural network, recursive second-order Volterra, and bilinear filters. To simplify the nonlinear structures, we specifically consider filters that use only nonlinear functional expansions of the past output samples. The behavior of these filters is analyzed in the framework of feedforward nonlinear active noise control of narrowband reference noises. In this environment, nonlinear secondary paths are involved and an acoustic feedback between the loudspeaker and the reference microphone is present.