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Sine-wave fitting is usually done with least-squares minimization in the time domain. This can be slow when the number of samples is large (105 - 106 or more). It is shown that the fit can be done more effectively in the frequency domain using the Fourier transform of windowed data. This paper shows that using a Blackman-Harris window, it is enough to process just a few samples around the sine peak. To obtain accurate results in analog-to-digital converter (ADC) characterization, the input signal has to meet strict conditions, namely, coherent sampling and uniform distribution of phases. It will be shown that the precision of the estimator is enough to determine if the signal meets the two aforementioned conditions, and sometimes, it provides even better results than the original time-domain least-squares estimator.