Variance of the cumulative histogram of ADCs due to frequency errors

The variance in the number of counts of the cumulative histogram, used for the characterization of ADCs with the histogram method, is calculated without any restrictions regarding frequency errors on the stimulus and sampling signals, number of periods periods of the stimulus signal and number of samples. This makes the approach here presented more general than the traditional one, used in IEEE 1057-1994 standard, where only a limited frequency error range is considered. The exact knowledge of this variance allows for a more efficient test of ADCs and a more precise determination of the uncertainty of the test result. Numerical simulation and experimental results that validate the theory are shown.