Bias of mean value and mean square value measurements based on quantized data

This paper investigates the imperfect fulfilment of the validity conditions of the noise model quantization. The general expressions of the deviations of the moments from Sheppard´s corrections are derived. Approximate upper and lower bounds of the bias are given for the measurement of first- and second-order moments of sinusoidal, uniformly distributed, and Gaussian signals. It is shown that because of the uncontrollable mean value at the input of the ADC (offset, drift), the worst-case values have to be investigated; it is illustrated how a simple-form envelope function of the errors can be used as an upper bound. Since the worst-case relative positions of the signal and the quantization characteristics are taken into account, the results are valid for both midtread and midrise quantizers, while in the literature results are given for a selected quantizer type only