Selecting test frequencies for sinewave tests of ADCs

A common requirement for the selection of a frequency for sinewave tests of waveform recorders or analog-to-digital converters (ADCs) is to make a selection that guarantees that the phases of the sampled values are uniformly distributed between 0 and 2π. It is well known that this requirement is met by choosing a frequency for which there is an exact integer number of cycles J~ in the record length M and that J~ is relatively prime to M. In this paper, we address the question of how well the phase uniformity is maintained when the frequency deviates slightly from its ideal value. We show that, in general, phase uniformity can be so sensitive to frequency deviations that it may be nearly impossible to attain. However, we show that there are special values of J~ for which the phase uniformity is relatively insensitive to frequency deviations. These are the values of J~ whose inverse, modulo M, is either very close to zero or very close to M.