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A computational scheme is developed for estimating the Doppler frequency of sinusoidal pulses based on Newton's method for finding the zero of a function. Time samples of the above pulse are processed via a FFT. The magnitude of the FFT outputs that cross a certain threshold along with the adjacent outputs are used to estimate the unknown frequency by a coherent centroiding scheme. Next Newton's method is applied to a Matched Filter "Test" function based on the centroiding estimator. It is shown that for sufficiently high SNR frequencies of sinusoids can be estimated by this technique with an accuracy approaching the Cramer-Rao bound with only 1 iteration of Newton's method. The computational load of the algorithm presented here is smaller by a factor of at least 10 over other conventional estimators. The algorithm provides a fast and accurate implementation of the Maximum Likelihood estimator.