Re: [time-nuts] ergodicity vs 1/f
In message , Magnus D anielson writes: Years ago I ran into this paper: https://fas.org/irp/agency/dod/jason/statistics.pdf What is amazing about it, is that back in 1992 they nailed the odds of climate change to north of 100k, in a statistically rigorous manner. They can do this because "Extreme Value Theory" is an extremely sensitive way to determine if a process is static or if it fits your (noise-)model. I've often wondered about EVTs applications to oscillator noise, but Real Life have kept me busy with other things, so I'll happily pass this ball to anybody else who might want a go... Poul-Henning -- Poul-Henning Kamp | UNIX since Zilog Zeus 3.20 p...@freebsd.org | TCP/IP since RFC 956 FreeBSD committer | BSD since 4.3-tahoe Never attribute to malice what can adequately be explained by incompetence. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] ergodicity vs 1/f
Hi On 12/18/2017 01:03 AM, Bob kb8tq wrote: 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 ….. 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 ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] ergodicity vs 1/f
Hi > On Dec 17, 2017, at 6:50 PM, Magnus Danielson > 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 > ___ > time-nuts mailing list -- time-nuts@febo.com > To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] ergodicity vs 1/f
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 ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] ergodicity vs 1/f (was: Allan variance by sine-wave fitting)
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. >You are mixing up ergodicity and reproducability. Also, you are moving the 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). > 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. >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. cheers, Mattia 2017-11-30 15:40 GMT+01:00 Attila Kinali : > On Thu, 30 Nov 2017 12:44:13 +0100 > Mattia Rizzi wrote: > > > 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 [ > > https://en.wikipedia.org/wiki/Ergodic_process] > > If it's ergodic, you can characterize the stochastic process using only > one > > realization. > > If it's not, your measurement is worthless, beca
Re: [time-nuts] ergodicity vs 1/f
Hi > On Nov 30, 2017, at 11:10 AM, Magnus Danielson > wrote: > > > > On 11/30/2017 03:40 PM, Attila Kinali wrote: >> On Thu, 30 Nov 2017 12:44:13 +0100 >> Mattia Rizzi wrote: >>> 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 [ >>> https://en.wikipedia.org/wiki/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. >> You are mixing up ergodicity and reproducability. >> Also, you are moving the 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. If you want to verify that your >> production lot has consistent performance metrics, then this is a >> completely different goal and requires a different methodology. But >> in the end it will boil down to measuring each clock/oscillator >> individualy to make sure it fullfils the specs. 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 >>> >>> Without ergodicity you cannot claim it. You have to suppose ergodicity. >> If 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. >> >>> If it's not stationary, it can change over time, therefore you are not >>> authorized to use a SA. It's like measuring the transfer function of a >>> time-varying filter (e.g. LTV system), the estimate doesn't converge. >> 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. > > After tons of measurements and attempts on theory a model was formed that was > sufficiently consistent with measurements. > > The model that fits observation makes much of the traditional statistical > measures and definitions "tricky" to apply. > > Flicker, that is PSD of 1/f, still is tricky to hunt down the real root and > model it, so we just use approximation in it's place because we need to have > something to work with. I believe that was roughly the third thing the prof said when he introduced 1/F noise back when I was in school. It *might* have been the fourth thing …. that was a long time ago …. Bob > Even without flicker, the white frequency noise messes with us. > > This thread seems to lost contact with these aspects. > > Cheers, > Magnus > ___ > time-nuts mailing list -- time-nuts@febo.com > To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] ergodicity vs 1/f
On 11/30/2017 03:40 PM, Attila Kinali wrote: On Thu, 30 Nov 2017 12:44:13 +0100 Mattia Rizzi wrote: 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 [ https://en.wikipedia.org/wiki/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. You are mixing up ergodicity and reproducability. Also, you are moving the 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. If you want to verify that your production lot has consistent performance metrics, then this is a completely different goal and requires a different methodology. But in the end it will boil down to measuring each clock/oscillator individualy to make sure it fullfils the specs. 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 Without ergodicity you cannot claim it. You have to suppose ergodicity. If 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. If it's not stationary, it can change over time, therefore you are not authorized to use a SA. It's like measuring the transfer function of a time-varying filter (e.g. LTV system), the estimate doesn't converge. 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. After tons of measurements and attempts on theory a model was formed that was sufficiently consistent with measurements. The model that fits observation makes much of the traditional statistical measures and definitions "tricky" to apply. Flicker, that is PSD of 1/f, still is tricky to hunt down the real root and model it, so we just use approximation in it's place because we need to have something to work with. Even without flicker, the white frequency noise messes with us. This thread seems to lost contact with these aspects. Cheers, Magnus ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
[time-nuts] ergodicity vs 1/f (was: Allan variance by sine-wave fitting)
On Thu, 30 Nov 2017 12:44:13 +0100 Mattia Rizzi wrote: > 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 [ > https://en.wikipedia.org/wiki/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. You are mixing up ergodicity and reproducability. Also, you are moving the 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. If you want to verify that your production lot has consistent performance metrics, then this is a completely different goal and requires a different methodology. But in the end it will boil down to measuring each clock/oscillator individualy to make sure it fullfils the specs. > >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 > > Without ergodicity you cannot claim it. You have to suppose ergodicity. If 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. > If it's not stationary, it can change over time, therefore you are not > authorized to use a SA. It's like measuring the transfer function of a > time-varying filter (e.g. LTV system), the estimate doesn't converge. 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. Attila Kinali -- It is upon moral qualities that a society is ultimately founded. All the prosperity and technological sophistication in the world is of no use without that foundation. -- Miss Matheson, The Diamond Age, Neil Stephenson ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
