maybe some one smarter than us can working with the parameters  that Tbolt
makes available better performance can be achieved but it is a fact  that
the frequency is being changed to compensate for time and Tom's frequency
data matches our's and we do not care about ADEV, we care about the actual
frequency at that moment it goes in to the measuring device and there is room
for improvement if you are a frequency nut and are looking for ways to
improve. Bob made a good point.

In a message dated 9/1/2016 4:27:02 P.M. Eastern Daylight Time,
csteinmetz@yandex.com writes:

Tom  wrote:

(antenna? reception? time constant? environment? China resoldered  parts?). I
appreciate that Juerg did lots of testing -- do you happen to have  his ADEV
plot?

I see. Something is wrong.

I second that  (not that any further evidence is necessary following
Tom's comprehensive  response).  Additionally, as far as I know, the
units Tom was testing  would have had the default tuning parameters (Tom,
please comment).  Most Tbolts I've seen can be tuned for much better
performance than this  at tau > 100 seconds, if they are equipped with a
37265  OCXO.

Note that the Tbolt has tuning parameters that limit how far the
frequency is allowed to wander to adjust the PPS phase -- if Bert's
unit(s) have these parameters set to allow very fast PPS recovery, that
could well cause the behavior he describes.

You should also check  all of the other tuning parameters to see if there
are errors in the  settings.

However, rather than mucking about in the myriad tuning  settings
starting where they are now, I recommend doing a full factory  reset to
get all parameters back to the original settings.  Then  (after several
weeks of undisturbed running), compare ADEV performance  with Tom's graphs.

Best  regards,

Charles

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Hi

The problem with absolute frequency is the one they ran into in the 60’s (and before):

There is no really good way to measure it.

You certainly can take data. The data can have lots of resolution.  That part has
always been fairly easy. The problem is that  the more carefully you look, the larger a
number you get. The number can grow 2, 3, 4, 5X as you look in more depth. There is
no nice simple way to limit the measurement so that does not happen. This makes it
a very hard thing to characterize.

Many frequency measurement systems have built in limits. They have a bandwidth (often
narrow). They have an integration time (sometimes FIR, sometimes IIR). They have internal
noise processes. All of that “colors” the result. This is in addition to the basics of observation
time and number of samples. Running two differently designed devices in parallel can result
in two very different “frequency readings”.

We do “hand waving” conversions of ADEV (or some other variance). That gives a number to
some number of decimal places. The gotcha is still that the underlying noise processes may or
may not be “nice enough” for the conversion to have any meaning. That issue has caught a lot
of people over the years. On things like GPSDO’s, the noise processes  rarely are “nice”. You
have humps and bumps from control loops and multiple noise sources. It’s a messy problem.

None of this really addresses the question of “how do I characterize absolute frequency”. It
simply goes back to the 1960’s and the whole reason we have ADEV. It is a quantity that
you can measure and the measure converges as you take more data. Absolute frequency
diverges as you take more data. Yes, the papers explain it a lot more clearly with a lot more
math.

Bob

Bert wrote:

I am quite sure of that

Yes, the PPS is steered by making slight adjustments to the OCXO
frequency.  But you can make these adjustments as arbitrarily small as
you want with the setup parameters.  I run my Tbolts with pretty tight
limits on the frequency adjustments.

There is no "there" there.  One never makes a frequency measurement at
just one instant -- the measurement will ALWAYS be done over a macro
time interval (very often, one second, sometimes 0.1, 10, 100, or 1000
seconds).  We never observe, and have no way to know, the instantaneous
frequency (as you put it, "the actual frequency at that moment it goes
into the measuring device") -- so how can we care about it?  The only
thing relevant (or even meaningful) is the average frequency during our
measurement interval.

xDEV tells us half of what we want to know -- how stable our oscillator
is from one measurement interval to another.  We would also like to know
what frequency it is wobbling around -- the "centroid" frequency, if you
will (to borrow a geometric term).  (Mathematicians can argue for days
about which type of "average" is appropriate here -- the rest of us just
pick one and carry on.)  ADEV does not tell us this "centroid" frequency
directly, but it can be extracted from the same measurements we took to
calculate ADEV.

I think you are being misled by a belief that the linguistic construct,
"instantaneous frequency," has real meaning in the world.  It doesn't.

Best regards,

Charles

Just a stupid question...

On a theoretical basis, can one speak of the limit of the frequency observed as tau approaches zero?

Might that in some way be the "instantaneous frequency" which people often think of?

I rather suspect the answer is "no," but I'll ask anyway.

Sent from my iPhone

Hi

Frequency is a "change over time". If delta time is zero it is undefined. As you observe it in shorter time periods, the accuracy / stability gets worse. Since the error bars expand there isn't much of a limit as you go shorter. They are not quite the same thing, but they are related.

Bob

Nick wrote:

That is (or is "something like") what it would be, but a little
thought experiment will show that (and why) the linguistic construction
is meaningless.

The period of a 10MHz sine wave is 100nS.  Think about observing it over
shorter and shorter (but still finite) time intervals.

When the time interval is 100nS, we see one complete cycle (360 degrees,
2 pi radians) of the wave.  At this point we still have some shot at
deducing its frequency, because no matter at what phase we start, we are
guaranteed to observe two peaks (one high, one low) and at least one
midpoint (e.g., zero-cross).  Our deduction (inference) will be less
accurate as the noise and distortion (harmonic content) increases, and
it won't be all that good under the best of circumstances.

Now shorten the observation time to 20nS.  We see 1/5 of a complete
cycle (72 degrees, 0.4 pi radians) of the wave.  No matter which
particular 72 degrees we see, we simply don't have enough information to
reliably deduce the frequency.  By sampling very fast (say, every
100fS), we at least know pretty well the trajectory of that little
snippet of signal, and using heroic measures we can make an educated
guess about the frequency -- but we really couldn't say we "knew" what
the frequency was.  Our error bars are growing, growing....

Now consider a 1nS sample.  Nothing we can do now will give us even a
bad guess as to the frequency.  And finally, consider a genuine
"instant" sample (one mathematical point of the wave form).  We have now
reached the point where there is literally NO information about the
frequency.  One time-voltage point could be part of a literally infinite
number of signals, each one of a different frequency from DC to infinity.

Thus we see that the well-formed English phrase, "instantaneous
frequency," is, literally, meaningless.  It denotes absolutely nothing.

Best regards,

Charles

On Fri, Sep 2, 2016 at 12:51 AM, Charles Steinmetz
csteinmetz@yandex.com wrote:

I do not see why you argue that.

For the purpose of discussion, lets assume you have a noiseless signal
which is stationary in frequency and amplitude over 20nS starting at
the zero crossing. Given these strong priors (single tone, constant
frequency which is not higher than one half cycle in our 20nS window,
constant amplitude, noiseless) there is exactly one frequency
consistent with any of those two observations.  If the starting phase
is unknown, I believe you need one additional observation to end up
over-determined and have an unambiguous solution again.

This kind of strong prior assumption is why sinusoidal estimators and
PLLs are able to extract tones with precision far beyond what you
would expect from taking a DFT from equivalent amount of data.

In reality, there is phase noise, non-linearities, harmonics, tidal
variations, and whatnot that make these assumptions untrue... but how
far they corrupt these assumptions depends on how useless the results
are.

Hi

Unfortunately if you read a typical text on FM modulation, "instantaneous frequency" comes up pretty fast. In that context it has a valid meaning. Once out of context, it gets you in trouble. That point is never made when the term is introduced.

Bob

On 9/1/16 5:51 PM, Charles Steinmetz wrote:

in fact, there's a whole literature on how accurate (or more precisely,
what's the uncertainty) of the frequency estimate is.

We often measure frequencies with less than a cycle - but making some
assumptions - measuring orbital parameters is done using a lot less than
a complete orbit's data, but we also make the assumption of the physics
involved.

Instantaneous frequency does have a theoretical meaning, even if not
measureable..

If I'm processing  a linear frequency chirp, I can say that the
frequency at time t is some (f0 + t*slope).  the frequency at time
t+epsilon is different, as is the frequency at time t-epsilon.

Jim wrote:

Strictly speaking, the chirp does not have a frequency, at any time --
it has a spectrum.  We use the mathematical fiction of "instantaneous
frequency" to express the limit as we differentiate.  This is the same
as the use of the term in connection with FM modulation, and it is an
abstraction -- not something real in the world (which is why it is not
measurable, not only as a practical matter, but even in principle.)

Best regards,

Charles