Inverse tangent based adaptive IIR notch filter

The inverse tangent based second-order adaptive IIR notch filter (ITANF) is presented in this paper. It is well known that the gradient-based adaptive IIR notch filter (ANF) has inherent low convergence speed due to the flattened error function. Moreover, the magnitude of error function depends on magnitude of sinusoid which implies that the speed of convergence of the gradient-based adaptive algorithm also depends on the magnitude of an input signal. To improve such drawback, the new inverse tangent based adaptive algorithm for a second order IIR notch filter is therefore proposed. The proposed algorithm employs the ratio of output to input signals as an error criterion where the inverse tangent value of the ratio is employed to adapt the filter parameter. It is found that the proposed algorithm provides not only high speed convergence but also high impulse noise robustness. The simulation results confirm that the performance of the proposed algorithm has been improved over the conventional ANF.