A new class of FLANN filters with application to nonlinear active noise control

FLANN and generalized FLANN filters exploiting trigonometric functions are often used in active noise control. However, they cannot approximate arbitrarily well every causal, time-invariant, finite-memory, nonlinear system, i.e., they are not universal approximators as the Volterra filters. In this paper, we propose a novel class of FLANN filters, called Complete FLANN filters, which satisfy the Stone-Weierstrass theorem, and thus can arbitrarily well approximate any nonlinear, time-invariant, finite-memory, continuous system. CFLANN filters are members of the class of nonlinear filters characterized by the property that their output depends linearly on the filter coefficients. As a consequence, they can be efficiently implemented in the form of a filter bank and adapted using algorithms simply derived from those applied to linear filters. In the paper, we apply a nonlinearly Filtered-X NLMS algorithm for CFLANN filters and describe some useful applications in the area of nonlinear active noise control.