Fast computation of time deviation and modified Allan deviation for telecommunications clock stability characterization

Time and frequency characterization of precision clocks and oscillators is an important task in the maintenance of time and frequency standards. Recently, time domain signal characterization of clocks is generally preferred and several performance measures of clocks and oscillators are defined in ITU-T Recommendation G.810. Among these measures, maximum time interval error (MTIE), time deviation (TDEV) and modified Allan deviation (MDEV) are frequently used, especially in telecommunications measurement. However, the direct computation of MTIE, TDEV and MDEV, defined in ITU-T Recommendation G.810, tends to be unmanageable when the number of samples becomes large. We propose a fast computation approach for TDEV and MDEV. The approach is based on the recursive algorithm and the computation exactly conforms to the ITU-T G.810 definition. As compared with the direct computation approach, the time complexity of the proposed approach is reduced by a factor of N, the number of samples. It reveals that the real-time measurement or monitoring will be feasible by employing the proposed computation approach