Resolution of F vs t measurement

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Discussion Overview

The discussion revolves around measuring the resolution of frequency measurements obtained from a resonator using a Laser-Doppler vibrometer and a frequency counter. Participants explore methods for determining the precision of these measurements, particularly in the context of fluctuations observed over time.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests using the RMS error as a universal method for stating errors in frequency measurement.
  • Another participant proposes calculating the Allan deviation as a function of integration time, arguing it provides a more accurate measure of frequency resolution.
  • A further contribution emphasizes that standard deviation may not be suitable for all noise types and recommends the Allan deviation as a more reliable alternative for this analysis.
  • Resources such as the NIST handbook of frequency analysis and Matlab routines for calculating Allan deviation are mentioned as helpful references.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate method for determining frequency resolution, with some advocating for RMS error and others favoring Allan deviation. No consensus is reached on which method is definitively superior.

Contextual Notes

Participants highlight that standard deviation may not converge properly for noise types other than white noise, indicating limitations in its applicability for this context.

Excom
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Hi all

I have measured the resonance frequency of a resonator as a function of time by mean of a Laser-Doppler vibrometer and a frequency counter. In this measurement there are some fluctuations in the measured frequency as time goes by.
My question is: How do I determine the resolution of this frequency measurement? Or in another way: How precise can I resolve the frequency? Do I take the standard deviation for a period and then define this as my frequency resolution?

I hope someone can help me.

Best regards
Excom
 
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That would be the RMS error. A pretty universal way of stating errors - I say go for it.
 
Thanks:-)
 
A more correct way of doing it is to calculate the Allan deviation as a function of integration time and then take the minimum value.
 
Indeed. the standard deviation is not a good measure in these situations. The reason is that it only converges for white noise, for all other noise types the STD will give you the "wrong" result which is why the Allen deviation should always be used for this type of analysis.

Have a look at the NIST handbook of frequency analysis (free download). Also, there are free Matlab routines for calculating the ADEV available on Mathworks file exchange.
 

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