NIST Technical Note 1337: Characterization of Clocks and Oscillators

12 FREOUENCV AND TIME MEASUREMENT215x(t),.!.., ,~~ I"IIIII ,! l' I I I !---..lI I ' :t ~:a .. 5 • 7'.. • 10 11 12 13 14'"Tl I NONOYERLAPPING y~ :~....."I--;"i FULLY OYERLAPPING i~..."aIt'TIMEFIG. 12-14 Illustration of the case of ': = 4'0_ for which the ralio of the number of fullyoverlapping to nonoverlapping estimates of the variance is more than 8 for the Si phase pointsshown. When the averaging time for the computation of mean frequencies 1 exceeds thesampling time 10. the number of fully overlapping mean frequencies is far larger than the numberof nono'·erlapping frequencies. In general. for large N approximately 2m times as manyestimates of the sample variances.can be computed using the fully overlapping technique.* TABLE12-4Number of Degrees of Freedom for Calculation of the Confidence of theEstimate of a Sample Allan Variance'!'ioise typeWhite phaseFlicker phaseWhite frequencydfIN + lX.'I/ - 2m)2lN - m)eX{In('\: I) In«1m + I~X,\j -I))J3(N - 1) 2(N - 21J 4m'[ ~ - --N-- 4m 2 + 52(N - 21Flicker freq uency for m = 12.3N - 4.9Random-walk frequency5N'4rrnN ~ 3mlfor m :2: 2N - 2 (N - 1)2 - 3m(.'V - I) + 4m 2m (N - 31=• For': = mro from .'1 phase points spaced '0 apart.* See Appendix Note # 39IN-85