[time-nuts] ergodicity vs 1/f

[Bob kb8tq]

Hi



> On Dec 17, 2017, at 6:50 PM, Magnus Danielson <magnus at rubidium.dyndns.org> wrote:
> 
> 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.

You then hit the very basic fact that a “standard noise process” does not cover what real oscillators or amplifiers
do in the field. They have a *lot* of “noise like” issues that impact their performance. Simply coming up with a model
for this or that process is only a very basic start to modeling a real device …..

Bob


> 
> Best Regards,
> Magnus
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