期刊
METROLOGIA
卷 52, 期 4, 页码 565-574出版社
IOP PUBLISHING LTD
DOI: 10.1088/0026-1394/52/4/565
关键词
frequency uncertainty; Allan deviation; clock comparison
资金
- German Research Foundation DFG [CRC 1128, RTG 1729]
- ITOC project in the European Metrology Research Programme EMRP
- QESOCAS project in the European Metrology Research Programme EMRP
- EMRP participating countries within EURAMET
- European Union
The power spectral density in the Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability of an oscillatory signal. It is often supposed that the statistical uncertainty of a measured average frequency is given by the ADEV at a well-considered averaging time. However, this approach requires further mathematical justification and refinement, which has already been done regarding the original ADEV for certain noise types. Here we provide the necessary background to use the modified Allan deviation (modADEV) and other two-sample deviations to determine the uncertainty of weighted frequency averages. The type of two-sample deviation used to determine the uncertainty depends on the method used for determination of the average. We find that the modADEV, which is connected with Lambda-weighted averaging, and the two-sample deviation associated with a linear phase regression weighting (parADEV) are, in particular, advantageous for measurements in which white phase noise is dominating. Furthermore, we derive a procedure for how to minimise the uncertainty of a measurement for a typical combination of white phase and frequency noise by adaptive averaging of the data set with different weighting functions. Finally, some aspects of the theoretical considerations for real-world frequency measurement equipment are discussed.
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