sys_fuzzMime-Version: 1.0

[Achim Gratz]

Eric S. Raymond writes:
> Is "unbiased and has a (relatively) white spectrum" equivalent to
> looking like symmetrical digital white noise around actual UTC, if you
> knew what it was?

Yes, if you knew the error exactly, then looking at it as a signal in
its own right.  The task of the PLL is to steer the error to zero and
the filtering that allows it to do this without undue overshoot or even
oscillations oscillations necessarily has a few assumptions about the
possible forms of error signal baked in.

"Unbiased" means that various forms of averaging should converge to
zero.  "Relatively White Spectrum" means that there shouldn't be any
concentrations of energy at specific frequencies within the loop
bandwidth of the PLL (equivalently that the Fourier spectrum in that
bandwidth is "flat").  Together these two conditions ensure, among other
things, that the average error converges to zero smoothly and that the
autocorrelation for the error signal stays close to zero for all time
lags.

Viewed from the other side: if you had a biased error signal, the PLL
would converge to a fixed offset to UTC that was representative of that
bias.  If the spectrum was not white, then the PLL would develop a
time-variable offset around UTC (which could end up as an oscillation).

> (I'm asking this question because my inituitions about analog-level
> signal processing are still weak.)

In this case we're talking about digital signals all the way, but it
doesn't make much of a difference for your question fortunately.


Regards,
Achim.
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