Fast computation of maximum time interval error by binary decomposition

The maximum time interval error (MTIE) is historically one of the main time-domain quantities for the specification of clock stability requirements in telecommunications standards. Nevertheless, plain computation of the MTIE standard estimator proves cumbersome in most cases of practical interest, due to its heavy computational weight. In this paper, MTIE is first introduced according to its standard definition. Then, a fast algorithm based on binary decomposition to compute the MTIE standard estimator is described. The computational weight of the binary decomposition algorithm is compared to that of the estimator plain calculation, showing that the number of operations needed is reduced to a term proportional to Nlog₂N instead of N². A heavy computational saving is therefore achieved, thus making feasible MTIE evaluation based on even long sequences of time error (TE) samples. The algorithm proposed is finally applied to TE sequences generated by simulation of all the types of power-law noise, in order to check its effectiveness and correctness