Hej Attila, On 10/26/18 11:50 AM, Attila Kinali wrote: > Hej Ole, > > On Fri, 26 Oct 2018 11:34:41 +0200 > Ole Petter Ronningen <[email protected]> wrote: > >> I'm simulating some noise to try to improve my somewhat sketchy >> understanding of what goes on with the various noise types as shown on an >> ADEV plot. Nothing fancy, ~3600 points of gaussian random numbers between 0 >> and 1 in excel, imported into Timelab as phase data, scaled to ns. >> >> I mostly get what I expect; "pure" random noise, gives the expected slope >> for W/F PM, -1. Integrating the same random data gives the expected slope >> for W FM -1/2. Integrating the same random data yet again gives a slope >> of +1/2, again as expected for RW FM. > > I see two issues here: If your random numbers are indeed between 0 and 1, > as you write, then they are uniformly distributed, and not normally > distributed. This will give you a slight bias when integrating.
Yes and no. It will not be relevant for ADEV values, but it will be relevant for the ADEV confidence intervals. > The other issue is the integration itself. Because you do a nummerical > integration at discrete time steps, you will get a slight offset. > This is something I stumbled over as well. I probably need to sit > down once, and figure out how big that offset should be and compare > it to what the numerical integration shows. The people here who are > more knowledgable than me about nummerical computation should be able to > give you a better answer. It's very simple. Integration in continuous time and in discrete time has somewhat different properties. I'm surprised that a stupid boy like me needs to point out to professional when they fluked on the difference, in peer-reviewed articles even. If you compare continuous time integration values with discrete time values you can expect a difference, as the devil is in the details. Now, to make it clear, ADEV is actually a discrete time measure, which we can approximate continuous time processes and behaviors with. Numerical integration is really not as such a bias-generating thing. You can end up with a scale error, so due care needs to be taken, but that ends up being fairly obvious once you think about things. Cheers, Magnus _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com and follow the instructions there.
