+1 to abtime
On Thu, Apr 20, 2017 at 1:35 PM, Tom Van Baak <[email protected]> wrote: > Jim Palfreyman writes: > > > Consider a plot of a timing residual vs time. Say a watch against a > maser, > > residual=watch-maser. > > We usually don't use the word residual for this. When you compare a watch > with a maser, or any DUT time against REF time, you get a quantity like: > phase difference, or sometimes just "phase", or time difference, time > error, time interval, time interval error, etc. > > What residual usually refers to is if you post-process the raw time or > frequency data in some way to better expose underlying structure. For > example, if you remove a linear or quadratic fit from your phase data the > resulting data set can be called phase residuals. This is done with > free-running clocks because both frequency, and especially phase, diverge > badly over time. So plotting residuals removes large systematic effects and > exposes small effects of interest. > > > > Now if I now plot the cumulative sum (think integral) of the residual, > > that's going to give me an overall view of how the clock is performing > over time. > > A traditional phase plot of residuals is itself "an overall view of how > the clock is performing over time". That's why even before we make ADEV > plots we want to see the phase (actually, phase difference) plot and maybe > also the frequency (usually, normalized frequency) plot. Both give an > overall view of how the clock is performing, not to mention the ADEV plot > which even further summarizes clock performance. > > A cumulative sum, an integral, of the timing residuals is a bit odd, but > not wrong. This is the "area under the curve" of any residual phase plot. A > traditional phase plot gives you a series of points on a line -- these tell > you your clock error as a function of elapsed time. But plots are 2D, so > your eye also senses the amount of area under the line -- this tells you > not only how far off your clock is, but how long your clock has been how > far off. The plot shows, and the eye recognizes both the line (how far) and > the area (how far x how long). > > > (If it helps, think of PID controllers and how they work in the "I" > part.) > > Yes, exactly. And the reason this is explicit in PID (or PIID) is that > there is no human eye and no 2D plot. Therefore the PID algorithm has to > manually compute the "area under the curve"; it has to calculate the > cumulative sum as a scaler value. And it sounds like this single scaler > value, as opposed to a rendered plot image, is what you're after. > > > > Now if you look at *motion* of an object over time, and you integrate its > > acceleration you get velocity, integrate again you get displacement. > > Integrate again and you get "absement" and again you get "abcity" (I only > > recently discovered these terms). > > Ok, thanks for that word of the day! Full list here: > > https://en.wikipedia.org/wiki/Absement#Higher_integrals > > > Does the integral of a timing residual have a name, and does the integral > > of *that* have a name as well? > > Nope. But let's make one up in honor of your time spent doing Pulsar work. > Some sources suggest absement is a portmanteau of absent and displacement. > Ok, could be, but just as likely ab- is a fine Latin prefix on its own, > meaning away, depart. Think of abnormal, abhor, absent, abdicate, aberrant. > Or the German abfahren, to depart from. (Ah, I finally got to put my Latin > and German to use; or is that abuse). > > https://en.wiktionary.org/wiki/ab- > http://membean.com/wrotds/ab-away > https://www.vocabulary.com/lists/135086 > > Anyway, in the world of space / distance: > > -4 abserk > -3 abseleration > -2 absity > -1 absement > 0 displacement > +1 velocity > +2 acceleration > +3 jerk > > So how about for the world of time, we call integrated phase error: > abtimer, or just abtime: > > -1 abtime (integrated phase error, cumulative sum of time error, etc.) > units: s^2 > 0 time (phase, time error, phase difference, etc.) units: s > +1 frequency (rate of phase change, etc.) units: /s, Hz > +2 drift (linear frequency change) units: /s^2, Hz/s > > I can imagine cases where abtime would be useful, especially for closed > loops. Units are seconds^2, or second*days, etc. For example, it may come > in handy when I post plots of the new WWVB receiver, or characterizing a > sloppy GPSDO timing receiver. > > /tvb > > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to https://www.febo.com/cgi-bin/ > mailman/listinfo/time-nuts > and follow the instructions there. > _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
