Frequency and Time - Their Measurement and Characterization

List of Symbols 12.1 Concepts, Definitions, and Measures of Stabilitv 12.1 .l Relationship between the Power Spectrum and the Phase Spectrum 12.1.2 The IEEE Recommended Measures of Frequency Stability 12.1.3 The Concepts of the Frequency Domain and the Time Domain 12.1.4 Translation between the Spectral Density of Frequency and the Allan Variance 12.15 The Modified Allan Variance 12.1.6 Determination of the Mean Frequency and Frequency Drift of an Oscillator 12.1.7 Confidence of the Estimate and Overlapping Samples 12.16 Efficient Use of the Data and Determination of the Degrees of Freedom 12 1.9 Separating the Variances of an Oscillator from the Reference 12.2 Direct Drgital Measurement 12.2.1 Time-Interval Measurements 12.2.2 Frequency Measurements 12 2.3 Period IMeasurements 12.3 Sensitivity-Enhancement Methods 12.3.1 Heterodyne Techmques 12.3.2 Homodyne Techniques 12 3.2.1 Discriminator and Delay Line 12 3.2 2 Phase-Locked Loop 12.3.3 Multiple Conversion Methods 12.3 3 1 Frequency Synthesis 12.3 3.2 The Dual-Mixer Time-Drfference Technique 12 333 Frequency Multiplication 12.4 Conclusion