A NEW MEMORYLESS NONLINEAR GRADIENT ALGORITHM FOR A 2ND-ORDER ADAPTIVE IIR NOTCH FILTER AND ITS PERFORMANCE ANALYSIS

Adaptive infinite inpulse-response (IIR) notch filters have been widel y studied for many years. However, further efforts are still to be mad e to pursue new algorithms which work better than the conventional pla in gradient algorithm but have little increase in complexity. In this paper, we employ the gradient linearization, Taylor series expansion, and calculus of variations to derive a novel memoryless nonlinear grad ient algorithm for a second-order adaptive IIR notch filter, which imp roves the estimation performance considerably. Approximate closed-form expressions for the stability bounds on the step size parameter and t he steady-state coefficient variance are also derived. Extensive simul ations indicate the significant improvement that may be achieved using the new algorithm, and verify the validity of the analytical results.