Uncertainty due to quantization error in measurement of Newton's constant with the angular acceleration method

The amplitude estimation of a sine signal with known frequency by the correlation method is biased in the presence of quantization error. An approximate analytical expression for the uncertainty as a function of the sine signal amplitude, the basic unit of quantization and the number of signal periods is obtained. As a comparison, the uncertainty due to general white Gaussian noise is also calculated. It is shown that in the experiment measuring G with the angular acceleration method, the uncertainty due to quantization error is evaluated to be less than that due to the additive thermal noise, which is somehow dependent on the experimental parameters.