Hi >This is true. But then the Fourier transformation integrates time from minus infinity to plus infinity. Which isn't exactly realistic either.
That's the theory. I am not arguing that it's realistic. >Ergodicity breaks because the noise process is not stationary. I know but see the following. >Well, any measurement is an estimate. It's not so simple. If you don't assume ergodicity, your spectrum analyzer does not work, because: 1) The spectrum analyzer takes several snapshots of your realization to estimate the PSD. If it's not stationary, the estimate does not converge. 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. 2017-11-27 23:50 GMT+01:00 Attila Kinali <[email protected]>: > Hoi Mattia, > > On Mon, 27 Nov 2017 23:04:56 +0100 > Mattia Rizzi <[email protected]> wrote: > > > >To make the point a bit more clear. The above means that noise with > > > a PSD of the form 1/f^a for a>=1 (ie flicker phase, white frequency > > > and flicker frequency noise), the noise (aka random variable) is: > > > 1) Not independently distributed > > > 2) Not stationary > > > 3) Not ergodic > > > > I think you got too much in theory. If you follow striclty the statistics > > theory, you get nowhere. > > You can't even talk about 1/f PSD, because Fourier doesn't converge over > > infinite power signals. > > This is true. But then the Fourier transformation integrates time from > minus infinity to plus infinity. Which isn't exactly realistic either. > The power in 1/f noise is actually limited by the age of the universe. > And quite strictly so. The power you have in 1/f is the same for every > decade in frequency (or time) you go. The age of the universe is about > 1e10 years, that's roughly 3e17 seconds, ie 17 decades of possible noise. > If we assume something like a 1k carbon resistor you get something around > of 1e-17W/decade of noise power (guestimate, not an exact calculation). > That means that resistor, had it been around ever since the universe was > created, then it would have converted 17*1e-17 = 2e-16W of heat into > electrical energy, on average, over the whole liftime of the universe. > That's not much :-) > > > In fact, 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. > > Well, any measurement is an estimate. > > > Every experimentalist suppose ergodicity on this kind of noise, otherwise > > you get nowhere. > > 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. > > > Attila Kinali > -- > <JaberWorky> The bad part of Zurich is where the degenerates > throw DARK chocolate at you. > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to https://www.febo.com/cgi-bin/ > mailman/listinfo/time-nuts > and follow the instructions there. > _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
