Adaptive recursive FLANN filters for nonlinear active noise control

In this paper, a recursive nonlinear filter exploiting trigonometric expansions of the past output samples is introduced. Its peculiarity is, in general, the ability to model real nonlinear systems with a reduced number of coefficients in comparison to finite-memory filters, as IIR filters often do in the linear case. However, the main drawback of recursive models is the need to guarantee, or at least verify, their bounded-input-bounded-output stability. In this paper, a sufficient stability condition is presented, showing that our recursive nonlinear filter is not affected by instabilities when the input signal has finite amplitude and the recursive linear part of the filter is stable. The filter has an interesting application in nonlinear feedforward active noise control since it is able to take into account the acoustic feed back between the loudspeaker, that generates the canceling sound, and the reference microphone, that senses the noise to be canceled, in presence of nonlinear effects. In the paper, a suitable nonlinear adaptation algorithm is derived in such a framework and then applied with good results to a realistic scenario.