Nonlinear adaptive recursive filtering using gradient-based algorithms

This paper presents a nonlinear adaptive recursive digital filter in which an adaptively adjustable nonlinear function is placed at the output of a linear recursive filter. Adaptive algorithms are based on a gradient search technique for updating coefficients of the filter and parameters of the nonlinear function. The filter is stable in the sense that the filter output is always bounded with bounded input signals, and it does not need stability monitoring in the adaptive process. Computer simulations confirm the validity of the derived results.