Ulrich, Don Ulrich Bangert wrote: > Don, > > >> What sort of SNR is necessary to prevent an uncertaincy >> of 1part in 10^13? >> > > 110dB or more for Tau = 1sec. > I see, you are a non believer! But Bruce was talking about comparing > zero crossings of signals at a few (!) Hz, which needs indeed tremendous > amounts of SNR to get to an uncertainity of 1 part in 10^13! The reason > is that for precice timing not the signal-to-noise-ratio is the figure > of merit but the slope-to-noise-ratio. > > With a 10 MHz signal and a 1 Hz signal having the same SNR the 1 Hz > signal will be inferior 10E7 in terms of slope-to-noise-ratio which > gives raise to the necessity of an 140 dB improved SNR on 1 Hz against > the 10 MHz signal if you want to measure the zero crossings with the > SAME incertainity as on the 10 MHz signal. > > If you are still critical about it: A zero crossing detector for a 1 Hz > signal giving a uncertainity of better than 1E-6 (some universes apart > from your 10E-13) has been celebrated as an first grade scientifical > breakthrough some years ago. > > Best regards > Ulrich Bangert > > P.S. > > Of course the above applies only to sinusoidal signal forms where the > slope of the zero crossings depends on the signal's frequency. So one > might pretend he is going to measure the zero crossings of DIGITAL > signals of a few Hz which may be indeed easy to measure due to their > high slew rates. The people that argument this way must ask themselves > how to make a digital signal from a sine signal which is pretty much the > same problem as measuring the zero crossing with high precision. > > > Bruce
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