  The estimation of the parameters of a dynamic signal, such as a sine wave,
based on quantized data is customarily performed using the least-square
estimator (LSE), such as the sine fit. However, the characteristics of the
experiments and the measurement setup hardly satisfy the requirements ensuring
the LSE to be optimal in the minimum mean-square-error sense. This occurs if
the input signal is characterized by a large signal-to-noise ratio resulting in
the deterministic component of the quantization error dominating the random
error component and when the ADC transition levels are not uniformly
distributed over the quantizer input range. In this paper, it is first shown
that the LSE applied to quantized data does not perform as expected when the
quantizer is not uniform. Then, an estimator is introduced that overcomes these
limitations. It uses the values of the transition levels so that a prior
quantizer calibration phase is necessary. The estimator properties are analyzed
and both numerical and experimental results are described to illustrate its
performance. It is shown that the described estimator outperforms the LSE and
it also provides an estimate of the probability distribution function of the
noise before quantization.
