Arctangent based adaptive algorithm for a complex IIR notch filter for frequency estimation and tracking

• A new arctangent based adaptive algorithm for a first-order complex IIR notch filter is proposed.
• This algorithm gives very low bias and is robust to both Gaussian and impulsive noises.
• Sinusoidal signal amplitude does not produce any effect to the algorithm.
• Mean analysis and computer simulations have been done to confirm the performances of the proposed algorithm.

An arctangent (AT) based adaptive algorithm for a first-order complex adaptive IIR notch filter (CANF) is proposed in this paper. The objective of this work is to overcome some drawbacks including slow convergence speed and high sensitivity to impulsive noise of the previous gradient and nongradient based adaptive algorithms. The proposed AT algorithm employs the ratio of output to regressor signal as an error criterion where the arctangent value of such a ratio is employed to adjust the filter parameter. It is found that the proposed algorithm provides not only high speed convergence but also high impulsive noise robustness. Moreover, very low bias of the frequency estimate is also obtained. In addition, difference equation for the convergence in the mean and coarse stability bound in mean sense are derived. Computer simulations are conducted to show the performance of the proposed AT algorithm.