  This paper considers least-square based estimation of the amplitude and
square amplitude of a quantized sine wave, done by considering random initial
record phase. Using amplitude- and frequency-domain modeling techniques, it is
shown that the estimator is inconsistent, biased and has a variance that may be
underestimated if the simple model of quantization is applied. The effects of
both sine wave offset values and additive Gaussian noise are taken into
account. General estimator properties are derived, without making simplifying
assumptions on the role of the quantization process, to allow assessment of
measurement uncertainty, when this least-square procedure is used.
