[time-nuts] Zero dead time and average frequency estimation

Bruce Griffiths bruce.griffiths at xtra.co.nz
Mon Feb 1 12:16:49 UTC 2010


Magnus Danielson wrote:
> Tom,
> Tom Van Baak wrote:
>> Magnus,
>> Correct, all the terms cancel between the end points. Note
>> that this is exactly equivalent to the way a traditional gated
>> frequency counter works -- you open the gate, wait some
>> sample period (maybe 1, 10, or 100 seconds) and then
>> close the gate. In this scenario it's clear that all the phase
>> information during the interval is ignored; the only points
>> that matter are the start and the stop.
> There is a technical merit to take samples in between even if they 
> cancel... you avoid counter overflow, but you can do better, much better.
>> Modern high-resolution frequency counters don't do this;
>> and instead they use a form of "continuous counting" and
>> take a massive number of short phase samples and create
>> a more precise average frequency out of that.
> Yes, and the main point for creating this little thread is to make 
> people aware that how you process your data do make a difference. It 
> can make a huge difference in fact. The effective two-point frequency 
> calculation only use two sample point to estimate the frequency and 
> thus also use the systematic value and noise of one sample to cancel 
> the noise of the first sample. For 1/f power noises this is an effect 
> that can even becomes larger (for 1/f^3 noise) with time as it is 
> non-convergent, so by looking at it briefly you don't realize it is a 
> noisy number.
>> There are some excellent papers on the subject; start with
>> the one by Rubiola:
>> < 
>> http://www.femto-st.fr/~rubiola/pdf-articles/journal/2005rsi-hi-res-freq-counters.pdf 
>> >
>> There are additional papers (perhaps Bruce can locate them).
> In particular, there is one paper that corrects some mistakes of 
> Rubiola, Australian if I remember correctly.
Yes, the paper by Dawkins, McFerran and Luiten:


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