Abstract
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.
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