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This paper analyzes the statistical performance of analog-to-digital converter (ADC) effective-number-of-bit (ENOB) estimators provided by sine-fitting algorithms. Accurate expressions for the estimator bias and standard deviation that hold regardless of the overall ADC output noise characteristics are derived. These expressions are then particularized for ADC output noise composed of tones (both harmonics and spurious tones) and additive white noise. Two specific cases of ideal ADCs and ADCs affected by harmonics, spurious tones, and additive white Gaussian noise are also analyzed. In particular, it is shown that, for values of the number of acquired samples commonly used in ADC testing practice, the sine-fitting ENOB estimators are statistically optimal since they are almost Gaussian, unbiased, and efficient. The accuracies of all the derived expressions are verified through both computer simulations and experimental results.