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Discrete Derivative Method for Adaptive Notch Filter-based Frequency Estimators

Jong-Min Yoon, Wook Bahn, Tae-Il Kim, Ji-Seok Han, Sang-Hoon Lee, and Dong-Il "Dan" Cho*
International Journal of Control, Automation, and Systems, vol. 15, no. 2, pp.668-679, 2017

Abstract : "This paper presents a new discrete derivative method for adaptive notch filter (ANF)-based frequency estimators. ANF-based frequency estimators are widely used for online frequency estimation because of their small computation requirements and simple structures. A discrete-time derivative is usually required for the estimators because they are implemented in the discrete-time domain. However, conventional discretization processes may cause problems in calculating the derivative of the adaptive filter state. For example, a derivative needs to have a phase 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 transform method can prevent the phase problem, but it has oscillating transient responses, which deteriorate the convergence properties of the estimated frequency. A new discrete derivative method that modifies the bilinear transform is proposed. 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 estimators that use the proposed derivative method can accurately estimate the frequencies of input signals in various frequency ranges."

Keyword : Adaptive notch filter, bilinear transform method, discrete derivative method, discretization, finite difference method, frequency estimator.

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