# [time-nuts] Name of integral of timing residual

Magnus Danielson magnus at rubidium.dyndns.org
Thu Apr 20 02:28:46 EDT 2017

```Hi,

On 04/20/2017 07:17 AM, Jim Palfreyman wrote:
> Folks,
>
> I'm after the formal name of something (if it exists), and this group, if
> any, should know.
>
> Consider a plot of a timing residual vs time. Say a watch against a maser,
> residual=watch-maser.
>
> 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. (If it helps, think of PID controllers and how they work in the "I"
> part.)
>
> 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).
>
> Does the integral of a timing residual have a name, and does the integral
> of *that* have a name as well?
>
> Any thoughts?

Wither it is timing residuals (time error (TE) or time interval error
(TIE) ) or time itself does not change the core of it being integrated time.

I have never heard of any definition for is, as we have for phase,
frequency and linear drift.

When considering similar problems with charge and current you end up
with As (or Ah) which is a measure of energy (assuming a voltage), often
referred to as capacity, but it doesn't really help.

In this case, integrated time error is what I would use. It is not as
catchy, but it is correct at least.

Cheers,
Magnus
```