A novel memoryless nonlinear gradient algorithm for a second-order adaptive IIR notch filter

Adaptive IIR notch filters have been widely studied for many years. However, not many efforts have been made to pursue new algorithms which work better than the plain gradient algorithm but have a little increase in complexity. In this paper, we employ the gradient linearization, Taylor series expansion and calculus of variations to derive a memoryless nonlinear gradient function for a second-order adaptive IIR notch filter, which improves the estimation performance considerably. Theoretical expressions for the stability bounds on the step size parameter and the steady-state coefficient variance of the proposed algorithm using the memoryless nonlinear gradient function are also derived. Extensive simulations indicate the significant improvement that may be achieved using the new algorithm, and verify the closed-form analytical results.