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[Eric S. Raymond]

Achim Gratz <Stromeko at nexgo.de>:
> 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.

I'd expect that on mathematical first principles, even though I don't
clearly understand how the "steering" works.  To steer you have to have
priors, some model of what "well-formed" looks like.

> "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").

Right, I got that part.  I do have some grasp of Fourier transforms
and frequency spectra, albeit mostly theoretical rather than
practical.  (I was a mathematician before I was a software engineer.)

>                        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).

OK, that was *useful*.  I had grasped the implications of bias, but I hadn't
clearly visualized  how a non-white error spectrum would cash out in the
time domain.  But it makes perfect sense to me now, yeah.  Your oscillating
error will correspond to where there's density in the error spectrum.

Thanks.
-- 
		<a href="http://www.catb.org/~esr/">Eric S. Raymond</a>