Hi,

Finally I have time to answer it properly.
Let's do a quick recap. Topic is flicker noise, statistics theory vs
experimental hypothesis. I am aware that flicker noise, in stochastic
theory, it's not ergodic nor stationary.

Mattia#1: (If you striclty apply the stochastic theory) you are not allowed
to take a realization, make several fft and claim that that's the PSD of
the process. But that's what the spectrum analyzer does, because it's not a
multiverse instrument.
Every experimentalist suppose ergodicity on this kind of noise (i.e.
flicker noise), otherwise you get nowhere.

Attila#1: Err.. no. Even if you assume that the spectrum tops off at some
very low frequency and does not increase anymore, ie that there is a finite
limit to noise power, even then ergodicity is not given.
Ergodicity breaks because the noise process is not stationary. And assuming
so for any kind of 1/f noise would be wrong.  the reason why this is wrong
is because assuming noise is ergodic means it is stationary. But the reason
why we have to
treat 1/f noise specially is exactly because it is not stationary.

Mattia:It's not so simple. If you don't assume ergodicity, your spectrum
analyzer does not work, because:

1. [...]
2. It's just a single realization, therefore also a flat signal can be a
   realization of 1/f flicker noise. Your measurement has zero statistical
   significance.

Attila#2: I do not see how ergocidity has anything to do with a spectrum
analyzer.
You are measuring one single instance. Not multiple.
A flat signal cannot be the realization of a random variable with a PSD ~
1/f. At least not for a statisticially significant number of time-samples.
If it would be, then the random variable would not have a PSD of 1/f. If
you go back to the definition of the PSD of a random variable X(ω,t), you
will see it is independent of ω.
And about statistical significance: yes, you will have zero statistical
significance about the behaviour of the population of random variables, but
you will have a statistically significant number of samples of one
realization of the random variable. And that's what you work with.

Mattia: Let me emphasize your sentence:  "you will have a statistically
significant number of samples of one realization of the random variable.".
This sentence is the meaning of ergodic process. If it's ergodic, you can
characterize the stochastic process using only one realization.
If it's not, your measurement is worthless, because there's no guarantee
that it contains all the statistical information.

End of recap.

Let's start again with Attila#2 in the recap. You say that a flat signal
cannot be a realization of flicker process. Well, you're using one
assumption "At least not for a statisticially significant number of
time-samples". This property is true only for an ergodic process.
Definition of ergodic process (from wikipedia): "a stochastic process is
said to be ergodic if its statistical properties can be deduced from a
single, sufficiently long, random sample of the process".
You applied ergodicy to dismiss my mental experiment. If you striclty apply
the stochastic theory, from an experimental point of view, you cannot proof
or dismiss hypothesis, which is the core of scientific research.

goalpost. We usually want to characterize a single clock or oscillator.
Not a production lot. As such the we only care about the statistical
properties of that single instance.

Nope. I was always talking about a single realization, coming from a
single DUT.
Due to the complex nature of flicker noise, you have just a single
realization in this Universe (thats why I am talking about multiverse in
Mattia#1).

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.

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.

cheers,
Mattia

2017-11-30 15:40 GMT+01:00 Attila Kinali attila@kinali.ch:

Hi,

On 12/17/2017 03:09 PM, Mattia Rizzi wrote:

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.

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

Hi

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

Hi

On 12/18/2017 01:03 AM, Bob kb8tq wrote:

Yes, indeed.

One does not have to be very esoteric. Temperature dependence is a very
systematic process, and we can kind of model a good part of its major
effects, but the "noise" of the temperature variations itself is not
easily covered and well, is a mess all in itself.

You then go downhill from there with gazillions sources of drift and
modulations.

We can however break some of the noise properties away and model them
and estimate their properties to some degree, so that helps get some of
the stuff understandable enough. The tools however is often widely
misunderstood and misused.

I just don't see how a lengthy debate on ergodicity is really helping
when doing it in the wrong end of things.

People does not even properly separate systematic effects from noise, so
their noise analyses becomes way of the mark and the systematic analyses
does not have proper confidence intervals. Then the discussing the color
of black does not help to understand the color of the orange very much.

Cheers,
Magnus