Online frequency estimation of a pure sinusoidal signal is a classical problem that has many practical applications. Recently an ANF with global convergence property has been developed, for this purpose. There exist some practical applications in which signals are not pure sinusoidal and contain harmonics. Therefore, online frequency estimation of periodic but not necessarily sinusoidal signals espoused by such applications becomes quite important. This note presents an alternative stability analysis for a modified ANF that permits the presence of harmonics in the incoming signal. Also, this stability analysis is simpler and alleviates the problem complexity even in the case of pure sinusoidal signal. Simulation results confirm theoretical issues.