A modified inverse tangent based adaptive algorithm for a second-order constrained adaptive IIR notch filter

• A new modified inverse tangent based adaptive algorithm for a second-order adaptive IIR notch filter is proposed.
• This algorithm is unbiased, robust to both Gaussian and impulsive noises.
• Sinusoidal signal parameters do not produce any effect to the algorithm.
• Mean analysis and computer simulations have been done to confirm the performances of the proposed algorithm.

A modified inverse tangent (MIT) based adaptive algorithm for a second-order constrained adaptive IIR notch filter (ANF) is proposed in this paper. The objective of this work is to overcome some drawbacks of the gradient based adaptive algorithms (GAs) including slow convergence speed, bias, and high sensitivity to impulsive noise. The proposed MIT algorithm employs the ratio of output signal to internal state as an error criterion where the inverse tangent value of such ratio is employed to adjust the filter parameter. It is found that the proposed algorithm provides not only high speed of convergence but also high impulsive noise robustness. Moreover, unbias of the frequency estimate is also obtained. Computer simulations are conducted to show the performance of the proposed algorithm.