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Online frequency estimation of a sinusoidal signal is a classical problem and has many practical applications. Recently an adaptive notch filter (ANF) with global convergence property has been developed for frequency estimation of a pure sinusoidal signal. This paper addresses a modified ANF structure that can estimate the fundamental frequency of any periodic signal including pure sinusoidal signals. To prove the stability of the modified ANF, the paper introduces a new theorem that shows for any periodic signal, there exists a locally asymptotically stable periodic orbit of this ANF by which the frequency estimation becomes feasible. This alternative stability proof is simple and uses widely known mathematical tools, and therefore alleviates the problem complexity even when the input signal is a pure sinusoidal signal. A further contribution of this paper is obtaining a necessary and sufficient condition in terms of …