  Slow fluctuations of a qubit frequency are one of the major problems faced by
quantum computers. To understand their origin it is necessary to go beyond the
analysis of their spectra. We show that characteristic features of the
fluctuations can be revealed using comparatively short sequences of
periodically repeated Ramsey measurements, with the sequence duration smaller
than needed for the noise to approach the ergodic limit. The outcomes
distribution and its dependence on the sequence duration are sensitive to the
nature of noise. The time needed for quantum measurements to display
quasi-ergodic behavior can strongly depend on the measurement parameters.
