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

[Bob kb8tq]

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 <mailto: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. 
>> >