[time-nuts] σ vs s in ADEV
Bob kb8tq
kb8tq at n1k.org
Mon Jan 9 18:20:48 EST 2017
Hi
> On Jan 9, 2017, at 5:09 PM, Jeremy Nichols <jn6wfo at gmail.com> wrote:
>
> 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.
The 5360A did ADEV. It only started being called ADEV after a few years had passed.
The 5360A program and it’s various quirks became the topic of a number of post paper
questions in the early 1970’s. The main focus of most of the questions was on bandwidth
limiting ahead of the counter. That question really didn’t get a proper answer for several
more decades.
Bob
>
> 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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