A fast and accurate adaptive notch filter using a monotonically increasing gradient

In this paper, we propose a new adaptive notch filter algorithm to achieve the fast and accurate narrow-band noise reduction. In the proposed algorithm, we introduce the monotonically increasing function into the gradient, which provides the fast convergence far away from the optical frequency. We additionally introduce the enhancement function into the gradient to design the steepness of the gradient curve. The proposed gradient can adjust the trade off between the convergence speed and the estimation accuracy more flexibly. Several computational simulations show that the proposed algorithm can simultaneously provide fast convergence and high accurate estimation compared with the conventional NLMS algorithm.