A system capable of generating every possible data frame subperiod and delayed subperiod of a data frame of length of M clock pulse intervals (CPIs) comprises parallel modulo-m.sub.i counters. Each m.sub.i is a prime power divisor of M. Each m.sub.i =p.sub.i .alpha..sub.i is a cascade of .alpha..sub.i identical modulo-p.sub.i counters, where m.sub.i p = p.sub.i .sup..alpha. . The modulo-p.sub.i counters are feedback shift registers which cycle through p.sub.i distinct states. By this organization, every possible nontrivial data frame subperiod (in terms of clock pulse intervals) and delayed subperiod may be derived. Also, a specific CPI in the data frame may be detected. The number of clock pulses required to bring every (or a subset of all) modulo-p.sub.i counter to a respective designated state or count is determined by The Chinese Remainder Theorem. This corresponds to the solution of simultaneous congruences over relatively prime moduli.
