Magnus
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:
http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F4318993%2F4318994%2F04319178.pdf%3Farnumber%3D4319178&authDecision=-203
<http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F4318993%2F4318994%2F04319178.pdf%3Farnumber%3D4319178&authDecision=-203>
Bruce
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