Hi folks, > (4) With four points you get change in drift over time. > The standard deviation of the drift prediction errors is > called the Hadamard Deviation.
you know that i like to advertise from time to time for it: My PLOTTER utility does compute the normal as well as the overlapping Hadamard deviation. It may be downloaded from http://www.ulrich-bangert.de/plotter.zip Cheers Ulrich, DF6JB > -----Ursprüngliche Nachricht----- > Von: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] Im Auftrag von Tom Van Baak > Gesendet: Donnerstag, 30. November 2006 19:26 > An: Mike Feher; 'Discussion of precise time and frequency measurement' > Betreff: Re: [time-nuts] Predicting clock stability > fromthevariouscharacterization methods > > > > Tom - > > > > Excellent description of the process. Glad you took the time to > > explain > this > > so clearly. While I do understand the process, I do not believe I > > could > have > > stated it so well. Not to nit pick, but you did make a > small typo in > > that you interchanged the predicted and measured value of > P2 in your > > example. > For > > most of us that will be obvious, and non relevant, but, to > some it may > > be confusing. Regards - Mike > > Ah, right. In the example, the prediction, P2', should > be 32 and the actual, P2, is 35; a prediction error of > 3 us. Thanks. > > ---- > > By the way, here's extra credit for some of you: > > (1) With one point you get phase, or time error. > > (2) With two points you get change in phase over time, > or frequency. > > (3) With three points you get change in frequency over > time, or drift. The standard deviation of the frequency > prediction errors is called the Allan Deviation. > > This is a measure of frequency stability; the better the > predicted frequency matches the actual frequency the lower > the errors. A little bit of noise or any drift causes the > errors to increase; the ADEV to increase. In the summation > you'll see terms like P2 - 2*P1 + P0. You can see why > constant phase offset or frequency offset doesn't affect the sum. > > (4) With four points you get change in drift over time. > The standard deviation of the drift prediction errors is > called the Hadamard Deviation. > > This is a measure of stability where even drift, as long > as it's constant, is not a bad thing. In the summation > you'll see P3 - 3*P2 + 3*P1 - P0. You can see why > constant phase, frequency, or even drift doesn't affect > the sum. > > ---- > > So imagine a situation where you're making a GPSDO > and very long-term holdover performance is a key design > feature. What OCXO spec is important? > > In this application phase error is easy to fix - you just > reset the epoch. > > Frequency error is easy to fix. After some minutes or > perhaps hours you get a good idea of the frequency > offset. You then just set the EFC DAC to a calculated > value and maintain it during hold-over. In this case the > OCXO with the lowest drift rate (best Allan Deviation) > is the one to choose. > > But with a little programming even drift is also easy to > fix. After some days or perhaps weeks you get a pretty > good idea of frequency drift over time and so you ramp > the EFC DAC over time to compensate. > > The only limitation to extended hold-over performance > in such a GPDO is irregularity in drift rate. > > In this example, the Hadamard Deviation would be a > good statistic to use to qualify the OCXO you need. > Drift, as long as it's constant (e.g., fixed, linear, even > log, or other prediction model) is not the limitation. > > /tvb > > > > _______________________________________________ > time-nuts mailing list > [email protected] > https://www.febo.com/cgi-> bin/mailman/listinfo/time-nuts > _______________________________________________ time-nuts mailing list [email protected] https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
