# [time-nuts] σ vs s in ADEV

Jeremy Nichols jn6wfo at gmail.com
Mon Jan 9 17:09:59 EST 2017

```In the late 1960s, Hewlett-Packard engineers worked up a program to have
the 5360A "Computing Pig" (so-called from its weight, 55 pounds without
plug-ins) compute a "fractional frequency standard deviation." It appears
to be similar to the Allen Deviation; I've never figured out the difference
and would appreciate hearing from someone with stronger math skills who can
explain the two.

Jeremy

On Mon, Jan 9, 2017 at 2:00 PM Bob kb8tq <kb8tq at n1k.org> wrote:

> Hi
>
>
>
> > On Jan 9, 2017, at 4:49 PM, Magnus Danielson <magnus at rubidium.dyndns.org>
> wrote:
>
> >
>
> > Scott,
>
> >
>
> > On 01/09/2017 07:41 PM, Scott Stobbe wrote:
>
> >> I could be wrong here, but it is my understanding that Allan's
> pioneering
>
> >> work was in response to finding a statistic which is convergent to 1/f
>
> >> noise. Ordinary standard deviation is not convergent to 1/f processes.
> So I
>
> >> don't know that trying to compare the two is wise. Disclaimer: I could
> be
>
> >> totally wrong, if someone has better grasp on how the allan deviation
> came
>
> >> to be, please correct me.
>
> >
>
> > There where precursor work to Allans Feb 1966 article, but essentially
> that where he amalgamed several properties into one to rule them all
> (almost). It is indeed the non-convergent properties which motivates a
> stronger method.
>
>
>
>
>
> A number of outfits were measuring and spec’ing short term stability in
> the 1950’s and early 1960’s. Some were doing measures that are pretty close
> to ADEV. Others were doing straight standard deviation of frequency
> measurements. Since both got tossed up as “short term stability” confusion
> was the main result. NIST came in (as it rightly should) and gave us a
> measurement that does converge. They also spend the next two decades
>
> thumping on a bunch of hard heads to get everybody to use the measurement
> rather than something with more issues. Once that effort was underway, we
> got a whole raft of alternatives that each have benefits in certain areas.
>
> ADEV is far from the only measure that could be properly be used today to
> characterize short term stability.
>
>
>
> Bob
>
>
>
> > Standard statistics is relevant for many of the basic blocks, bit things
> work differently with the non-convergent noise.
>
> > Another aspect which was important then was the fact that it was a
> counter-based measure. Some of the assumptions is due to the fact that they
> used counters. I asked David some questions about why the integral looks
> the way it does, and well, it reflects the hardware at the time.
>
> >
>
> > What drives Allan vs. standard deviation is that extra derive function
> before squaring
>
> > The bias functions that Allan derives for M-sample is really the
> behavior of the s-deviation. See Allan variance wikipedia article as there
> is good references there for the bias function. That bias function is
> really illustrating the lack of convergence for M-sample standard
> deviation. The Allan is really a power-average over the 2-sample standard
> deviation.
>
> >
>
> > Cheers,
>
> > Magnus
>
> >
>
> >> On Wed, Jan 4, 2017 at 3:12 PM, Attila Kinali <attila at kinali.ch> wrote:
>
>
>
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