Dynamic Signal Measurements Based on Quantized Data

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.