Educational and Practical Resources
The field of time and frequency and its use of Allan variance, Allan deviation and friends is a field involving many aspects, for which both understanding of concepts and practical measurements and post-processing requires care and understanding. Thus, there is a realm of educational material stretching some 40 years available. Since these reflect the developments in the research of their time, they focus on teaching different aspect over time, in which case a survey of available resources may be a suitable way of finding the right resource.
The first meaningful summary is the NBS Technical Note 394 "Characterization of Frequency Stability". This is the product of the Technical Committee on Frequency and Time of the IEEE Group on Instrumentation & Measurement. It gives the first overview of the field, stating the problems, defining the basic supporting definitions and getting into Allan variance, the bias functions B1 and B2, the conversion of time-domain measures. This is useful as it is among the first references to tabulate the Allan variance for the five basic noise types.
A classical reference is the NBS Monograph 140 from 1974, which in chapter 8 has "Statistics of Time and Frequency Data Analysis". This is the extended variant of NBS Technical Note 394 and adds essentially in measurement techniques and practical processing of values.
An important addition will be the Properties of signal sources and measurement methods. It covers the effective use of data, confidence intervals, effective degree of freedom likewise introducing the overlapping Allan variance estimator. It is a highly recommended reading for those topics.
The IEEE standard 1139 Standard definitions of Physical Quantities for Fundamental Frequency and Time Metrology is beyond that of a standard a comprehensive reference and educational resource.
A modern book aimed towards telecommunication is Stefano Bregni "Synchronisation of Digital Telecommunication Networks". This summarises not only the field but also much of his research in the field up to that point. It aims to include both classical measures likewise telecommunication specific measures such as MTIE. It is a handy companion when looking at telecommunication standard related measurements.
The NIST Special Publication 1065 "Handbook of Frequency Stability Analysis" of W.J. Riley is a recommended reading for anyone wanting to pursue the field. It is rich of references and also covers a wide range of measures, biases and related functions that a modern analyst should have available. Further it describes the overall processing needed for a modern tool.
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