Discrete Derivative Method for Adaptive Notch Filter-based Frequency Estimators

This paper presents a new discrete derivative method for adaptive notch filter (ANF)-based frequencyestimators. ANF-based frequency estimators are widely used for online frequency estimation because of their smallcomputation requirements and simple structures. A discrete-time derivative is usually required for the estimatorsbecause they are implemented in the discrete-time domain. However, conventional discretization processes maycause problems in calculating the derivative of the adaptive filter state. For example, a derivative needs to have aphase of 90◦, but finite difference methods produce phase responses that are less than 90◦ in high-frequency ranges. This phenomenon causes inaccurate frequency estimation results in high-frequency ranges. A bilinear transformmethod can prevent the phase problem, but it has oscillating transient responses, which deteriorate the convergenceproperties of the estimated frequency. A new discrete derivative method that modifies the bilinear transform isproposed. The proposed method does not produce the oscillating transient response in the steady state. Moreover,the phase responses of this method remain at 90◦ even in high-frequency ranges. Therefore, the frequency estimatorsthat use the proposed derivative method can accurately estimate the frequencies of input signals in various frequencyranges.