[time-nuts] ergodicity vs 1/f

Magnus Danielson magnus at rubidium.dyndns.org
Sun Dec 17 18:50:19 EST 2017


Hi,

On 12/17/2017 03:09 PM, Mattia Rizzi wrote:
>> you demand ergodicity, you cannot have 1/f. You can have only one or the
> other. Not both. And if you choose ergodicity, you will not faithfully
> model a clock.
> 
> I am talking about the issues of flicker noise processes for an
> experimentalist. I know that the (current) theory is incompatible with
> ergodicy, but for an experimentalist ergodicity is an assumption that you
> have to do. You did as well, in Attila#2.

We need to assume the properies of our model is static as we measure it 
and try to estimate the model parameters.

However, the noise we have does not have the normal convergence 
properties, so much of the normal ways of defining things does not 
directly apply.

Much of the methods we have come out of experimentalists trying to make 
models and methods adapt to their measurement reality.

A spectrum analyzer will pre-filter flicker noise and by that change its 
statistical behavior, it will start to behave much more like white 
noise, but there will be a bias in the reading. The bias in the reading 
depends on the filtershape and noise type. This is known from both 
theory and actual measurements.

Similarly will counter-based observation behave.

This heated debate on ergodic etc. needs to focus on what actually 
happens and leave the theory draftingboard, since honestly, you guys to 
not make enough sense even to me. Leave the fancy definitions aside for 
a moment and let's focus on the properties and how we achieve them and 
how not to achieve them.

>> Please take one of the SA's you have at CERN, measure an oscillator
> for a long time and note down the center frequency with each measurement.
> I promise you, you will be astonished.
> 
> Let's keep the focus on flicker noise, for instance, flicker noise of an
> amplifier. Noise in oscillators is more fuzzy.

It's the noise of oscillators you need to handle, because it will be 
there to act as test signals for amplifiers.

It is however understood and we have methods to handle it.

The models we have work within some limits. I've spent time to learn 
these limits and checked it with those knowing much better. Being 
rigorous about this is not for the fainthearted, and while many knows 
some, it does not help if you want to be rigorous. Then again, very very 
few are. I have not seen any real convergence in your debate, it's kept 
fluctuating without stabilizing just as a RMS measure does on these 
noisetypes, you keep deviating even wilder even.

I find that much of the terms and definitions in classical statistics is 
really not applicable as you encounter 1/f and further noises. While 
useful background, as you enter the dark dungeon of time and frequency, 
there be flicker dragons and other monsters that the classical 
statistics didn't prepare you very well for, even if it was a good 
education.

To go further, for a while all references to ergodic, I.I.D., gaussian 
etc. just have to pause, because they are not contributing to 
understanding, they only contribute to disagreement. Let's discuss 
actual properties separate, and maybe we can come back and conclude what 
it means in other terms, but not now.

Best Regards,
Magnus


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