[time-nuts] σ vs s in ADEV

Bob kb8tq kb8tq at n1k.org
Mon Jan 9 17:00:01 EST 2017


> 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.


> 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:

More information about the time-nuts mailing list