An apparatus and process for measuring, testing, and/or characterizing high-speed bit streams includes repeating a serial bit steam and repetitively undersampling the repeated bit stream at a plurality of timing locations. Samples for each timing location are separately accumulated, and accumulated values are examined to determine the probability of the bit stream being high or low at each timing location. Identification of a periodic bit stream as well as measurement of jitter and other timing characteristics can then be measured.