I look forward to the article, Magnus! Don Magnus Danielson > Fellow time-nuts, > > Since I haven't seen any reports on this, I though I would write down a > few lines. > > While normal counters use a pair of phase-samples to estimate the > frequency, now called Pi counters (big pi, which has the shape of the > weighing function of frequency samples), counter vendors have been > figuring out how to improve the precision of the frequency estimation > for the given observation time. One approach is to overlay multiple > measurements in blocks, which for the frequency estimation looks like a > triangle-shape weighing, so this type of counter is referred to as Delta > counters (again to resemble the shape). > > Classical counters of the Pi shape is HP5370A, SR620 etc. > Classical counter of the Delta shape is the HP53132A. > > However, counters using the Linear Regression methodology does not fit > into either of those categories. Enrico Rubiola derived the parabolic > shape of the weighing function (which I then independently verified > after we spoke during EFTF 2014), and he then passed on the results to > Francois Vernotte and other colleagues to continue the analysis. > > The new weighing function is a parabolic, looking like an Omega sign, so > that is the name for this type of counter. > > Counters using the Omega shape is HP5371A, HP5372A, Pendelum CNT-90, > CNT-91 etc. > > These weighing shapes acts like filters, and the block variant of the Pi > weighing has no real filtering properties, where as both the Delta and > Omega shapes has strong low-pass properties, which is beneficial in that > they will suppress white phase noise strongly, and that is the typical > measurement limitation of counters. The counter resolution limit also > acts like white phase noise even if it is a systematic noise, which can > interact in interesting ways as we have seen when signal frequencies has > interesting relationships to the reference frequency. However, for cases > when this is not true, the weighing helps to reduce that noise too from > the measurements. > > For frequency estimation this is good improvements. This technique was > actually introduced in optical measurements, as illustrated by J.J. > Snyder in his 1980 and 1981 articles. This inspired further development > of the Allan Variance to include the filtering technique of Snyder, and > that resulted in the Modified Allan Variance (MVAR). Today we refer to > the Snyder technique as the Delta counter. > > What Rubiola, Vernotte et. al discovered was that using a Linear > Regression (LR) type of frequency estimated for variance estimation > forms a new measure which they ended up calling Parabolic Variance > (PVAR). They have done a complete analysis of PVAR properties (noise > response and EDF) and it has benefits over MVAR. > > Variance made by a Delta counter thus becomes MVAR, but only as a > special case. > Variance made by a Omega counter becomes PVAR, but only as a special case. > > This is my main critique of their work, if you have access to the full > stream of phase samples, you can form MVAR and PVAR using the two > shaping techniques. However, if you use counters that perform these > frequency estimations, then you can only correctly estimate variance of > the two methods for the tau0 of the measurement result rate (and > assuming that you know if they are back to back or interlaced, which is > a mistake that was done at one time). If you have an Omega counter that > produce frequency estimates and then process it further, the parabolic > filtering shape does not change with m as it should for propper PVAR. > This is exactly the same as using a Delta counter for frequency > estimates and then perform variance estimation. For both cases, the > counter will provide a fixed filtering bandwidth, but as you increase > the m*tau0 for your analysis, the frequencies of your sample series will > move into the pass-band of the low-pass filter and eventually the > filtering effect is completely lost. The result is the hockey-puck > response where the low-tau part of the ADEV/MDEV/PDEV curve first > increases and then bends down to the white phase noise of the input as > if it was not filtered. > > While Vernotte et al does not provide guidance for how to extend the > PVAR from shorter measurements, I have proposed such a solution to them. > Unfortunatly none of the existing counters will support that today. > > Why then, should one use PVAR? Well, PVAR does give good suppression of > white flicker noise, and just as MVAR does has a 1/tau^3 curve rather > than 1/tau^2 curve. This means that the measurement noise can be > suppressed more effectively and the source noise can be reached for a > lower tau. PVAR will have a 3/4 of MVAR for the white phase nosie, so > there is a 1.25 dB improvement there. > > So, while it may read it from their papers that you get the PVAR from > Omega counters, it's not the same in their analysis where the filtering > function changes with m as you have with a typical counter which runs at > fixed m. This is not to say that the PVAR technique is not useful. > > Getting proper results with these types of techniques takes care in the > detail, but if you do you can harvest their benefits. > > For further reading, please check these articles: > > E. Rubiola, On the measurement of frequency and of its sample variance > with high-resolution counters (PDF, 130 kB), Rev. Sci. Instrum. vol.76 > no.5 article no.054703, May 2005. ©AIP. Open preprint > arXiv:physics/0411227 [physics.ins-det], December 2004 (14 pages, PDF > 220 kB). > http://rubiola.org/pdf-articles/journal/2005rsi-hi-res-freq-counters.pdf > > The Omega Counter, a Frequency Counter Based on the Linear Regression > http://www.researchgate.net/publication/278419387_The_Omega_Counter_a_Frequency_Counter_Based_on_the_Linear_Regression > > Least-Square Fit, Ω Counters, and Quadratic Variance > http://www.researchgate.net/publication/274732320_Least-Square_Fit__Counters_and_Quadratic_Variance > > The Parabolic variance (PVAR), a wavelet variance based on least-square fit > http://www.researchgate.net/publication/277665360_The_Parabolic_variance_%28PVAR%29_a_wavelet_variance_based_on_least-square_fit > > I should probably shape this up into a proper article. > > 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. > >
-- "If you don't know what it is, don't poke it." Ghost in the Shell ------------------------------- "Noli sinere nothos te opprimere" Dr. Don Latham, AJ7LL Six Mile Systems LLC, 17850 Six Mile Road Huson, MT, 59846 mailing address: POBox 404 Frenchtown MT 59834-0404 VOX 406-626-4304 CEL 406-241-5093 Skype: buffler2 www.lightningforensics.com www.sixmilesystems.com _______________________________________________ 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.