Hej Ole! On 10/28/18 9:19 AM, Ole Petter Ronningen wrote: > Hi, Magnus! > > Thank you for this! I am of course nowhere near really comprehending it > from reading it a couple of times, but I will still show my ignorance by > asking a couple of questions with respect to the power law noise table.
Please ask. > Counting on your day being still non-grumpy.. :D :-D > 1. I notice the formulas for ADEV is different for W PM and F PM - ADEV > does not distinguish between the two, as is pointed out in the article. > Does this not imply a fixed relationship between the power coefficients h1 > and h2, such that the results of those to formulas are the same? Or am I > misunderstanding the point of the table? (Also, what is the parameter > y/gamma in the FPM formulas?) The trouble is that the mathematical difference as you see in the table is very very hard to make use of, as you have two functions with almost the same shape, and the difference between them is small, so small that the confidence interval for the noisy type of data make it hard to extract the difference with any form of useful trust in the numbers. Add that you have other forms of disturbances which isn't pure noise. For most practical purposes they are indistinguishable using ADEV and this annoyed David Allan for 15 years until he finally could present the modified Allan, which is "the one" for him, as it is more complete in the noise separation aspect, which was the driver for his work in the first place. So, the table is correct, but not very useful in this regard. Remember that it is noisy data, and for any finite series of noisy data, there is practical limits to how much we can derive out of them. We keep inventing better tools to gain precision, reduce processing, reduce length of measurement etc. Thus, theoretical differences may turn out not be very useful in the practical world, so we need to do things in a way that is practical. When using MDEV you has an algorithmic bandwidth that change, which so for higher tau you have a more narrow-band filter, which makee white phase noise change amplitude much faster than flicker phase noise, and hence the distinction can be made. As you move over to parabolic deviation, it has even steeper filter and thus suppress noise even more. This helps to explain the improved performance of regression based frequency estimation. So, ADEV is far from the right tool for everything. In fact, it is greatly misused. > 2. I am not sure I understand the concept of f_H correctly, particularly as > it applies to synthetic data. What is the corner frequency of a random > sequence [0-1]? If you say that your samples is at tau_0=1s, then the sample-rate becomes f_S = 1/tau_0 = 1 Hz and the f_H becomes f_H = f_S * 1/2 = 1/2 Hz. 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.
