Rapid calculation of time deviation and modified allan deviation for characterizing telecommunications clock stability

Time and frequency characterization of precision clocks and oscillators is important in maintaining time and frequency standards. The recent preference has been for the time domain signal characterization of clocks, and several performance measures of clocks and oscillators are defined in ITU-T Recommendation G.810. The most frequently used of these measures are maximum time interval error (MTIE), time deviation (TDEV) and modified allan deviation (MDEV), especially in telecommunications measurement. However, the direct computation of MTIE, TDEV and MDEV, defined in ITU-T Recommendation G.810, tends to be unmanageable with a large number of samples. A fast computation approach for TDEV and MDEV is proposed herein. The proposed approach is based on an iterative algorithm and the computation conforms exactly to the ITU-T G.810 definition. Compared to the direct computation approach, the complexity of the proposed approach is reduced by a factor of N, or the number of samples. This characteristic reveals that real-time measurement or monitoring is feasible when the proposed computation approach is employed.