Discrete-derivative method for adaptive-notch-filter based frequency estimators

This paper presents a new discrete-derivative method for adaptive-notch-filter (ANF) based frequency estimators to reduce frequency estimation errors. Frequency estimators generally require the first derivative of the filter state. However, differentiating the filter state in the discrete-time domain can result in large estimation errors. If a finite difference method is used, the frequency estimation results in a large amount of errors when the input signal contains high frequency components. The bilinear transform method does not cause the high frequency problems, but causes an oscillation problem due to the finite poles and zeros used to approximate the continuous differentiation operation. In this paper, a modification of the bilinear transform method is proposed. The proposed method can differentiate the high frequency signal without the oscillation problem. Numerical simulations are performed, and the results show the effectiveness of the proposed method.