A piloted adaptive notch filter

In this paper, we propose a new adaptive system where the main zero of the notch filter is sandwiched between two piloted zeros. The gradient of the cost function provides information on the direction that the main zero should be steered towards the input sinusoid frequency. The piloted zeros are used to provide an indication on the distance between the frequency of the sinusoid and the zero location of the main notch filter. This information is used to control the adaptive step-size, for fast convergence if the frequency of the sinusoid is far away from the main zero of the notch and for small misadjustment if that distance is small. The technique is very effective for locking on frequencies, which are neither very close to dc nor very close to half sampling frequency. The complexity of the piloted filter is comparable to the conventional normalized LMS (NLMS) notch filter.