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A fast algorithm to estimate the frequency of a sinusoid is presented here. It is based on Newton's method for finding the root of an equation, and it is shown that under easily met conditions, the root mean-square error (RMSE) of the estimator is practically equal to the Cramer-Rao bound after only two iterations of Newton's method for all signal-to-noise ratios (SNR's) above threshold. The estimator's probability density function is computed analytically, and the RMSE is calculated for one and two iterations of Newton's method. Its computational load is shown to be significantly less than other conventional algorithms.