IEEE 1139-2008 pdf download IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology—Random Instabilities
2. Definitions
For the purposes of this standard, the following terms and definitions apply. The Authoritative Dictionaryof IEEE Standards Terms (B511 should be referenced for terms not defined in this clause. lf ambiguities arecreated between the narrative definition given here and the mathematical equation given in the text, theequation has priority.
2.1 amplitude spectrum S.(): One-sided spectral density of the normalized amplitude fluctuations,asdefined in normalized amplitude fluctuations a(t).
2.2 bias: The difference between the expected value of an estimator of a statistic and its correct value.
2.3 confidence interval: An interval of uncertainty associated with an estimate of an instability measurefrom a finite number of measurements. The endpoints of a confidence interval are called confidence limits.
2.4 frequency spectrum S,(): One-sided spectral density of the normalized frequency fluctuations, asdefined in normalized frequency fluctuations y(f).
2.5 normalized amplitude fluctuations a(t): Instantaneous normalized amplitude departure from anominal amplitude.
2.6 normalized frequency fluctuations y(f): Instantaneous, normalized frequency departure from anominal frequency.
2.7 phase fluctuations (f): Instantaneous phase departure from a nominal phase.
2.8 phase noise 0(f): One-half of the phase spectrum S (/), as defined in phase spectrum S()
2.9 phase spectrum S (): One-sided spectral density of the phase fluctuations
2.10 time fluctuations x(f): Instantaneous time departure from a nominal time
2.11 time interval error (TIE): The time difference between a real clock and an ideal uniform time scalefollowing a time period i after perfect synchronization.
2.12 time spectrum S(/): One-sided spectral density of the time fluctuations
2.13 two-sample deviation (): Also called the Allan deviation; the square root of the two samplevariance, as defined in two-sample variance o(t).
2.14 two-sample variance (c): Also called the Allan variance; one-half the time average of the squareof the difference between the averages of normalized frequency fluctuations over two adjacent timeintervals oflength t, with no dead time between the two averaging intervals.
3. Standards for characterizing or reporting measurements of frequency.amplitude,and phase instabilities
The standard measure for characterizing frequency and phase instabilities in the frequency domain is L()(pronounced “script-ell of f), defined as one half of the one-sided spectral density of phase fluctuations: