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A new approach in the design of digital algorithms for simultaneous local system magnitude and frequency estimation of a signal with time-varying frequency is presented. The algorithm is derived using the maximum likelihood method. The pure sinusoidal voltage model was assumed. The investigation has been simplified because the total similarity to the state of the problem of dc offset and frequency estimation has been noticed. Finite impulse response (FIR) digital filters are used to minimize the noise effect and to eliminate the presence of harmonic effects. The algorithm showed a very high level of robustness, as well as high measurement accuracy over a wide range of frequency changes. The algorithm convergence provided fast response and adaptability. This technique provides accurate estimates in about 25 ms and requires modest computations. The theoretical bases of the technique are described. To demonstrate the performance of the developed algorithm, computer-simulated data records are processed. The proposed algorithm has been tested in a laboratory to establish its feasibility in a real-time environment.