Hej Anders! On 10/28/18 1:14 PM, Anders Wallin wrote: > I made a revised figure with a few improvements: > - the PSDs now cross at 1Hz > - the theoretical ADEV/MDEV pre-factors are now explicitly stated > http://www.anderswallin.net/2018/10/noise-colours-again/ > source: > https://github.com/aewallin/colorednoise/blob/master/example_noise_slopes2.py
This is a great illustration of what we have been discussing. Notice that while the phase and frequency power densities neatly cross at 1 Hz, the Allan Deviation and Modified Allan Deviation does not cross at 1 s, in fact the cross-point between two noise-types is unique for that pair, but around the same point. The scale factors is due to how the details of the integration comes out. > I forget where the MDEV-coefficients come from - maybe the Dawkins et al. > paper? (worth adding to wikipedia also?) Let me dig into that. I did that for ADEV and biases, and there is a fair amount of copy from someone else, with some minor reformulations. The biases for instance ended up with a rarely mentioned NIST publication. > Also for flicker-PM there seems to be (slightly) different versions of the > ADEV pre-factor in different references. Yes, I've seen that too. For the Wikipedia I chose the more accurate one, where as various forms of short-hands have been used. They are all consistent as I recall it, but the difference is how they express the value. Some combine the two constants into a single number, where as if you do the integration you get three numbers, of which one depends on tau and f_H. It is worth mentioning that for WPM and FPM the integral does not converge if allowed to go to infinite frequency, so the integral needs to stop at the highest frequency f_H. The others do converge for infinite frequency so the integrals continue to infinity rather than stopping at f_H. So, the factors is not even created under the same circumstances. On the other hand, for all practical matters I expect them to be fairly close. 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.
