Adaptive IIR notch filter by frequency estimation for notch Fourier transform

This paper presents a method to compute Fourier coefficients at arbitrary frequencies. The method is developed for the case that prior knowledge of signal frequencies is not accurate or the frequencies are time varying and additive white noise exists. A less computationally complex algorithm of adaptive constrained IIR notch filters connected in cascade is proposed. The main advantages are as follows: (1) perpetrations of adaptive parameters is reduced, because of estimating notch frequencies by using a recursive LMS algorithm not intermediately from filter coefficients but directly from signal samples; (2) by the feedback of notch frequencies estimated by a less-biased overdetermined frequency estimation method to adaptive parameters, the convergence speed and the perturbation after convergence are improved.