[time-nuts] Re: Testing frequency pulling on a DYI counter

[Magnus Danielson]

Hi,

I am talking about very recent research that was presented at the 
IFCS-EFTF 2022 and also published as an UFFC article.

The observation is that the second derivative phase data is independent, 
so you can reuse samples as long as the phase & frequency transition is 
respected and that no pair of frequency estimates re-occur which can be 
achieved. The biases and quality tests turn out being really good.

The basic assumption is also what is used to prove that overlapping ADEV 
measures is independent and thus can be used without creating bias to 
the ADEV, but rather, is just a better estimator for ADEV.

The actual code is on github.

Cheers,
Magnus

On 8/7/22 23:02, Bob kb8tq wrote:
> Hi
>
> There are a lot of ways to deal with gaps. The best one is not to
> have them in the first place :). It is not uncommon to ignore the
> gap, but that does create issues. It also is not uncommon to plug
> in “average” data. Again, issues are created. The hope is that they
> are not as significant as ignoring it. How you generate that average
> data …. that depends …..
>
> So, no perfect solutions once you have a gap. If a setup produces
> gaps on a regular basis, that’s probably not a really good way to
> do things.
>
> Bob
>
>> On Aug 7, 2022, at 12:54 PM, Magnus Danielson <magnus at rubidium.se> wrote:
>>
>> Erik,
>>
>> OK, so it's not big magic really. There is an assumed time-base 
>> length. The actual time each such time-stamp is done shifts around a 
>> little. For a 10 MHz signal, the time-base shifts around within one 
>> period so 100 ns. The actual trigger point 1 and actual trigger point 
>> 2 will on average be the tau_0 time-distance from each other. As we 
>> do this for a set of frequency estimations and average these, it 
>> averages out. This is the basic assumption being used in all 
>> estimations I've seen. My algorithm makes no different assumption 
>> than any of the others I've seen.
>>
>> I have seen those processing this with more detail of actual delay, 
>> but that is when focusing on single-measurements. The danger there is 
>> that numeric precision eats you quickly.
>>
>> Now, the variation you get is really a systematic play on the period 
>> time and the tau_0 and the phase-ramp you get out of that. This 
>> breaks down into other phase-ramps of diminishing frequency and 
>> amplitude, just as in a DDS. This systematic pattern rolls of quickly 
>> in averaging while random noise does not roll off as quickly. The 
>> systematic pattern can be "nulled" by matching average length to 
>> pattern length, as always. You can't really resolve this systematic 
>> noise before you know the relationship, rather it is a consequence of 
>> the actual rational number and how you choose to measure it. Random 
>> noise tends to smooth things out.
>>
>> You need to compare the noise of the tau_0 "instability" with that of 
>> the signal and the time-interval measurement error, it's fairly small 
>> compared to the others together typically.
>>
>> Now, the algorithm you have in that paper does not handle gaps in 
>> data. It assumed a continuous block. Essentially the linear ramp of 
>> phase and frequency needs to be unbroken or it will be producing the 
>> wrong results. You can handle gaped data by altering the algorithm, 
>> it will be a little more messy, but still maintain most of the 
>> benefits. Gaped data is a big thing, and valuable work has been done 
>> for ADEV by Dave Howe.
>>
>> Cheers,
>> Magnus
>>
>> On 8/7/22 22:21, Erik Kaashoek wrote:
>>> Magnus,
>>> Now you confuse me.
>>> Can you simplify the calculation assuming the samples are equally 
>>> spaced even if they are not? Can you assume the spread is noise and 
>>> it will sjaal out? How about gaps?
>>> Please help me to understand
>>> Erik
>>>
>>> On Sun, Aug 7, 2022, 22:08 Magnus Danielson <magnus at rubidium.se> wrote:
>>>
>>>     Erik,
>>>
>>>     They never are. It's a running assumption that everyone makes.
>>>
>>>     Cheers,
>>>     Magnus
>>>
>>>     On 8/7/22 13:28, Erik Kaashoek wrote:
>>>     > Magnus,
>>>     > Due to the design of the counter it is not possible to
>>>     guarantee all
>>>     > captures are at exactly tau_0 distance.
>>>     > Erik.
>>>     >
>>>     > On 6-8-2022 22:09, Magnus Danielson wrote:
>>>     >> The linear algebra trick actually jumps behind the linear
>>>     algebra
>>>     >> using the knowledge that measurements is a sequence of tau_0
>>>     >> distance, and that allows significant reduction of the math
>>>     into a
>>>     >> much more benign form. It also creates benign decimation
>>>     methods that
>>>     >> you can apply to any form of your liking.
>>>     >
>>>
>