References for Frequency Stability Analysis

 

·      Notes

  1. These references are arranged by topic and sorted by date.
  2. All of the FCS and UFFC references are available on-line for IEEE UFFC members.
  3. Only the 1990 and later PTTI proceedings are now available on-line.
  4. None of the EFTF or older IEEE I&M proceedings are available on-line.
  5. Please report any suggestions or errors to W. J. Riley.

 

·      General

  1. Special Issue on Frequency Stability, Proc. IEEE, Vol. 54, Feb. 1966.
  2. Proc. IEEE, Vol. 55, June 1967.
  3. J.A. Barnes, “Atomic Timekeeping and the Statistics of Precision Signal Generators,” IEEE Proceedings, vol. 54, pp. 207-219, 1966.
  4. J.A. Barnes, et. al., “Characterization of Frequency Stability”, IEEE Trans. Instrum. Meas., Vol. IM-20, No. 2, pp. 105-120, May 1971.
  5. B.E. Blair (Editor), "Time and Frequency: Theory and Fundamentals", NBS Monograph 140, U.S. Department of Commerce, National Bureau of Standards, May 1974.
  6. G. Winkler, "A Brief Review of Frequency Stability Measures", Proc. 8th PTTI Meeting, pp. 489-527, Dec. 1976.
  7. J. Rutman, "Oscillator Specifications: A Review of Classical and New Ideas", Proc. 31th Annu. Symp. on Freq. Contrl., pp.291-310, June 1977.
  8. J. Vanier and M. Tetu, "Time Domain Measurement of Frequency Stability", Proc. 10th PTTI Meeting, pp. 247-291, Nov. 1978.
  9. P.Lesage and C. Audoin, “Characterization and Measurement of Time and Frequency Stability”, Radio Science, Vol. 14, No. 4, pp. 521-539, 1979.
  10. D.A. Howe, D.W. Allan and J.A. Barnes, "Properties of Signal Sources and Measurement Methods'', Proc. 35th Annu. Symp. on Freq. Contrl., pp. 1-47, May 1981. Also available on line at NIST web site.
  11. V.F. Kroupa (Editor), Frequency Stability: Fundamentals and Measurement, IEEE Press, Institute of Electrical and Electronic Engineers, New York, 1983, ISBN 0-87942-171-1.
  12. S.R. Stein, "Frequency and Time - Their Measurement and Characterization'', Chapter 12, pp.191-416, Precision Frequency Control, Vol. 2, Edited by E.A. Gerber and A. Ballato, Academic Press, New York, 1985, ISBN 0-12-280602-6.
  13. Proc. IEEE, Vol. 74, Jan. 1986.
  14. C.A. Greenhall, "Frequency Stability Review", Telecommunications and Data Acquisition Progress Report 42-88, Oct-Dec 1986, Jet Propulsion Laboratory, Pasadena, CA, pp. 200-212, Feb. 1987.
  15. D.W. Allan, “Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators”, IEEE Trans. Ultrasonics, Ferroelectrics and Freq. Contrl., Vol. UFFC-34, No. 6, pp. 647-654, Nov. 1987.
  16. D.W. Allan, et al., "Standard Terminology for Fundamental Frequency and Time Metrology", Proc. 42nd Annu. Freq. Control Symp., pp. 419-425, June, 1988.
  17. D.B Sullivan, D.W Allan, D.A. Howe and F.L.Walls (Editors), "Characterization of Clocks and Oscillators", NIST Technical Note 1337, U.S. Department of Commerce, National Institute of Standards and Technology, March 1990.
  18. D.W. Allan, “Characterization of Precision Clocks and Oscillators”, Class Notes, NRL Workshop, Nov. 1990.
  19. D.W. Allan, "Time and Frequency Metrology: Current Status and Future Considerations'', Proc. 5th European Freq. and Time Forum, pp. 1-9, March 1991.
  20. Special Issue on Time and Frequency, Proc. IEEE, Vol. 79, July 1991.
  21. J. Rutman and F. L. Walls, "Characterization of Frequency Stability in Precision Frequency Sources", Proc. IEEE, Vol. 79, July 1991.
  22. J.A. Barnes, "The Analysis of Frequency and Time Data", Austron, Inc., Dec. 1991.
  23. C.A. Greenhall, "The Generalized Autocovariance: A Tool for Clock Statistics", Telecommunications and Mission Operations Progress Report, Vol. 42-137, Jet Propulsion Laboratory, Pasadena, CA, May 1999.
  24. C. Audoin and B. Guinot, The Measurement of Time, Cambridge University Press, 2001.
  25. G.E.P. Box and G.M. Jenkins, Time Series Analysis: Forecasting and Control, San Francisco: Holden-Day, 1970.
  26. W.J. Riley, "The Basics of Frequency Stability Analysis", Hamilton Technical Services.
  27. W.J. Riley, "The Calculation of Time Domain Frequency Stability”, Hamilton Technical Services.
  28. W.J. Riley, “Techniques for Frequency Stability Analysis”, Tutorial at the 2003 Intl. Freq. Cont. Symp., May 2003.

 

·      Standards and Specifications

  1. "Characterization of Frequency and Phase Noise", Report 580, International Radio Consultative Committee (C.C.I.R.), pp. 142-150, 1986.
  2. MIL-PRF-55310, Oscillators, Crystal, General Specification For.
  3.  R.L. Sydnor (Editor), “The Selection and Use of Precise Frequency Systems”, ITU-R Handbook, 1995.
  4. Guide to the Expression of Uncertainty in Measurement, International Standards Organization, 1995, ISBN 92-67-10188-9.
  5. "IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology - Random Instabilities", IEEE Std 1139-1999, July 1999.

 

·      Classic (Pre-Allan variance)

  1. Proc. IEEE-NASA Symp. on the Definition and Measurement of Short-Term Frequency Stability, NASA SP-80, Nov. 1964.

 

·      Allan Variance

  1. D.W. Allan, "Allan Variance", Allan's TIME.
  2. D.W. Allan, "The Statistics of Atomic Frequency Standards'', Proc. IEEE, Vol. 54, No. 2, pp. 221-230, Feb. 1966.
  3. "Characterization of Frequency Stability", NBS Technical Note 394, U.S Department of Commerce, National Bureau of Standards, Oct. 1970.
  4. J.A. Barnes, et al, "Characterization of Frequency Stability", IEEE Trans. Instrum. Meas., Vol. IM-20, No. 2, pp. 105-120, May 1971.
  5. J.A. Barnes, “Variances Based on Data with Dead Time Between the Measurements”, NIST Technical Note 1318, U.S. Department of Commerce, National Institute of Standards and Technology, 1990.
  6. C.A. Greenhall, "Does Allan Variance Determine the Spectrum?", Proc. 1997 Intl. Freq. Cont. Symp., pp. 358-365, June 1997.
  7. C.A. Greenhall, “Spectral Ambiguity of Allan Variance”, IEEE Trans. Instrum. Meas., Vol. IM-47, No. 3, pp. 623-627, June 1998.
  8. D.A. Howe, "Interpreting Oscillatory Frequency Stability Plots", Proc. 2000 IEEE Freq. Contrl. Symp., pp. 725-732, May 2002

 

·      Modified Allan Variance

  1. D.W. Allan and J.A. Barnes, "A Modified Allan Variance with Increased Oscillator Characterization Ability", Proc. 35th Annu. Symp. on Freq. Contrl., pp. 470-474, May 1981.
  2. P. Lesage and T. Ayi, “Characterization of Frequency Stability: Analysis of the Modified Allan Variance and Properties of Its Estimate”, IEEE Trans. Instrum. Meas., Vol. IM-33, No. 4, pp. 332-336, Dec. 1984.
  3. C.A. Greenhall, "Estimating the Modified Allan Variance", Proc. 1995 IEEE Freq. Contrl. Symp., pp. 346-353, May 1995.
  4. C.A. Greenhall, "The Third-Difference Approach to Modified Allan Variance", IEEE Trans. Instrum. Meas., Vol. IM-46, No. 3, pp. 696-703, June 1997.
  5. C.A. Greenhall, "A Shortcut for Computing the Modified Allan Variance", Proc. 1992 IEEE Freq. Contrl. Symp., pp. 262-264, May 1992.

 

·      Time Variance and Time Error Prediction

  1. D.W. Allan and H. Hellwig, “Time Deviation and Time Prediction Error for Clock Specification, Characterization, and Application”, March 1981.
  2. D.W. Allan, D.D. Davis, J. Levine, M.A. Weiss, N. Hironaka, and D. Okayama, "New Inexpensive Frequency Calibration Service From NIST'', Proc. 44th Annu. Symp. on Freq. Contrl., pp. 107-116, June 1990.
  3. D.W. Allan, M.A. Weiss and J.L. Jespersen, "A Frequency-Domain View of Time-Domain Characterization of Clocks and Time and Frequency Distribution Systems'', Proc. 45th Annu. Symp. on Freq. Contrl., pp. 667-678, May 1991.

 

·      Hadamard Variance

  1. Jacques Saloman Hadamard (1865-1963), French mathematician.
  2. W.K. Pratt, J. Kane and H.C. Andrews, "Hadamard Transform Image Coding", Proc. IEEE, Vol. 57, No. 1, pp.38-67, Jan. 1969.
  3. R.A. Baugh, "Frequency Modulation Analysis with the Hadamard Variance", Proc. 25th Annu. Symp. on Freq. Contrl., pp. 222-225, April 1971.
  4. B. Picinbono, "Processus a Accroissements Stationnaires", Ann. des telecom, Tome 30, No. 7-8, pp. 211-212, July-Aug, 1975.
  5. K. Wan, E. Visr and J. Roberts, "Extended Variances and Autoregressive Moving Average Algorithm for the Measurement and Synthesis of Oscillator Phase Noise", 43rd Annu. Symp. on Freq. Contrl., pp.331-335, June 1989.
  6. S.T. Hutsell, "Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation", Proc. 27th PTTI Meeting, pp. 291-302, Dec. 1995.
  7. S.T. Hutsell, "Operational Use of the Hadamard Variance in GPS", Proc. 28th PTTI Meeting, pp. 201-213, Dec. 1996.
  8. D.N. Matsakis and F.J. Josties, "Pulsar-Appropriate Clock Statistics", Proc. 28th PTTI Meeting, pp. 225-236, Dec. 1996.
  9. W.J. Riley, “The Hadamard Variance”, Hamilton Technical Services, 1999.
  10. D. Howe, et al., “A Total Estimator of the Hadamard Function Used For GPS Operations”, Proc. 32nd PTTI Meeting, Nov. 2000, (to be published).

 

·     Modified Hadamard Variance

  1. S. Bregni and L. Jmoda, "Improved Estimation of the Hurst Parameter of Long-Range Dependent Traffic Using the Modified Hadamard Variance", Proceedings of the IEEE ICC, June 2006.
  2. C.A. Greenhall and W.J. Riley, "Uncertainty of Stability Variances Based on Finite Differences", Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting, December 2003.

 

·      Total Variance

  1. D.A. Howe, "An Extension of the Allan Variance with Increased Confidence at Long Term," Proc. 1995 IEEE Int. Freq. Cont. Symp., pp. 321-329, June 1995.
  2. D.A. Howe and K.J. Lainson, "Simulation Study Using a New Type of Sample Variance," Proc. 1995 PTTI Meeting, pp. 279-290, Dec. 1995.
  3. D.A. Howe and K.J. Lainson, "Effect of Drift on TOTALDEV", Proc. 1996 Intl. Freq. Cont. Symp. , pp. 883-889, June 1996
  4. D.A. Howe, "Methods of Improving the Estimation of Long-term Frequency Variance," Proc. 1997 European Frequency and Time Forum, pp. 91-99, March 1997.
  5. D.A. Howe & C.A. Greenhall, "Total Variance: A Progress Report on a New Frequency Stability Characterization", pp. 39-48, Proc. 1997 PTTI Meeting, Dec. 1997.
  6. D.B. Percival and D.A. Howe, "Total Variance as an Exact Analysis of the Sample Variance", Proc. 1997 PTTI Meeting, Dec. 1997.
  7. C.A. Greenhall, D.A. Howe and D.B Percival, “Total Variance, an Estimator of Long-Term Frequency Stability”, IEEE Trans. Ultrasonics, Ferroelectrics and Freq. Contrl., Vol. UFFC-46, No. 5, pp. 1183-1191, Sept. 1999.
  8. D.A. Howe, "Total Variance Explained", Proc. 1999 Joint Meeting of the European Freq. and Time Forum and the IEEE Freq. Contrl. Symp., pp. 1093-1099, April 1999.
  9. D.A. Howe, “The Total Deviation Approach to Long-Term Characterization of Frequency Stability”, IEEE Trans. Ultrasonics, Ferroelectrics and Freq. Contrl., Vol. UFFC-47, No. 5, pp. 1102-1110, Sept. 2000.
  10. D.A. Howe and T.K. Peppler, "Definitions of Total Estimators of Common Time-Domain Variances", Proc. 2001 Intl. Freq. Cont. Symp. , pp. 127-132, June 2001.

 

·      Modified Total Variance

  1. D.A. Howe and F. Vernotte, "Generalization of the Total Variance Approach to the Modified Allan Variance", Proc. 31th PTTI Meeting, pp.267-276, Dec. 1999.

 

·      Time Total Variance

  1. M.A. Weiss and D.A. Howe, “Total TDEV”, Proc. 1998 IEEE Int. Freq. Cont. Symp., pp. 192-198, June 1998.

 

·      Thêo1, ThêoBR, and ThêoH

  1. D.A. Howe and T.K. Peppler, "Very Long-Term Frequency Stability: Estimation Using a Special-Purpose Statistic", Proceedings of the 2003 IEEE International Frequency Control Symposium , pp. 233-238, May 2003.
  2. D.A. Howe and T.N. Tasset, "Thê01: Characterization of Very Long-Term Frequency Stability", Proc. 2004 EFTF .
  3. D.A. Howe, "ThêoH: A Hybrid, High-Confidence Statistic that Improves on the Allan Deviation", Metrologia 43 (2006), S322-S331.
  4. D.A. Howe, J. McGee-Taylor and T. Tasset, "ThêoH Bias-Removal Method", Proc. 2006 IEEE Freq. Contrl. Symp., pp. 788-792, June 2006.

 

·      MTIE

  1. P. Travella and D. Meo, “The Range Covered by a Clock Error in the Case of White FM”, Proc. 30th Annu. PTTI Meeting, pp. 49-60, Dec. 1998.
  2. P. Travella, A. Dodone and S. Leschiutta, “The Range Covered by a Random Process and the New Definition of MTIE”, Proc. 28th Annu. PTTI Meeting, pp. 119-123, Dec. 1996.
  3. Bregni, " Clock Stability Characterization and Measurement in Telecommunications”, IEEE Trans. Instrum. Meas., Vol. IM-46, No. 6, pp. 1284-1294, Dec. 1997.
  4. Bregni, " Measurement of Maximum Time Interval Error for Telecommunications Clock Stability Characterization”,  IEEE Trans. Instrum. Meas., Vol. IM-45, No. 5, pp. 900-906, Oct. 1996.
  5. G. Zampetti, “Synopsis of Timing Measurement Techniques Used in Telecommunucations”, Proc. 24th PTTI Meeting, pp. 313-326, Dec. 1992.
  6. M.J. Ivens, "Simulating the Wander Accumulation in a SDH Synchronisation Network", Master's Thesis, University College, London, UK, November 1997.
  7. S. Bregni and S. Maccabruni, "Fast Computation of Maximum Time Interval Error by Binary Decomposition", IEEE Trans. I&M, Vol. 49, No. 6, pp. 1240-1244, Dec. 2000.

 

·      Multi-Variance Analysis

  1. F. Vernotte, E. Lantz, "Time Stability: An Improvement of the Multi-Variance Method for the Oscillator Noise Analysis", Proc. 6th European Frequency and Time Forum, pp. 343-347, March 1992.
  2. F. Vernotte, E. Lantz, J. Groslambert and J.J. Gagnepain, "A New Multi-Variance Method for the Oscillator Noise Analysis", Proc. 46th Annu. Symp. on Freq. Contrl., pp. 284-289, May 1992.
  3. F. Vernotte, E. Lantz, J. Groslambert and J.J. Gagnepain, "Oscillator Noise Analysis: Multivariance Measurement", IEEE Trans. Instrum. Meas., Vol. IM-42, No. 2, pp. 342-350, April 1993.
  4. F. Vernotte, E. Lantz, F. Meyer and F. Naraghi, "Simultaneneous Measurement of Drifts and Noise Coefficients of Oscillators: Application to the Analysis of the Time Stability of the Millisecond Pulsars" Proc. 1997 European Frequency and Time Forum, pp. 91-99, March 1997.
  5. T. Walter, "A Multi-Variance Analysis in the Time Domain", Proc. 24th PTTI Meeting, pp. 413-424, Dec. 1992.

 

·      Dynamic Stability

  1. L. Galleani and P. Tavella, "The Characterization of Clock Behavior with the Dynamic Allan Variance", Proc. 2003 Joint FCS/EFTF Meeting, pp. 239-244.
  2. L. Galleani and P. Tavella, "Tracking Nonstationarities in Clock Noises Using the Dynamic Allan Variance", Proc. 2005 Joint FCS/PTTI Meeting.

 

·      Confidence Intervals

  1. J.A. Barnes and D.W. Allan, Variances Based on Data with Dead Time Between the Measurements", NIST Technical Note 1318, U.S. Department of Commerce, National Institute of Standards and Technology, 1990.
  2. C.A. Greenhall, "Recipes for Degrees of Freedom of Frequency Stability Estimators'', IEEE Trans. Instrum. Meas., Vol. 40, No. 6, pp. 994-999, Dec. 1991.
  3. M.A. Weiss and C. Hackman, "Confidence on the Three-Point Estimator of Frequency Drift'', Proc. 24th Annu. PTTI Meeting, pp. 451-460, Dec. 1992.
  4. M.A.Weiss and C.A. Greenhall, "A Simple Algorithm for Approximating Confidence on the Modified Allan Variance and the Time Variance", Proc. 28th Annu. PTTI Meeting, pp. 215-224, Dec. 1996.
  5. D.A. Howe, "Methods of Improving the Estimation of Long-Term Frequency Variance", Proc. 11th European Freq. and Time Forum, pp. 91-99, March 1997.
  6. W.J. Riley, “Confidence Intervals and Bias Corrections for the Stable32 Variance Functions”, Hamilton Technical Services, 2000.
  7. F. Vernotte and M. Vincent, "Estimation of the Uncertainty of a Mean Frequency Measurement”, Proc. 11th European Freq. and Time Forum, pp. 553-556, March 1997.
  8. P. Lesage and C. Audoin, “Characterization of Frequency Stability:  Uncertainty due to the Finite Number of Measurements”, IEEE Trans. Instrum. Meas., Vol. 22, No. 2, pp.157-161, June 1973.
  9. P. Lesage and C. Audoin, “Estimation of the Two-Sample Variance with a Limited Number of Data”, Proc. 31st Freq. Contrl. Symp., pp. 311-318, June 1977.
  10. K. Yoshimura, “Degrees of Freedom of the Estimate of the Two-Sample Variance in the Continuous Sampling Method”, IEEE Trans. Instrum. Meas., Vol. 38, No. 6, pp. 1044-1049, Dec. 1989.
  11. C.R. Ekstrom and P.A. Koppang, “Error Bars for Three-Cornered Hats”, IEEE Trans. Ultrasonics, Ferroelectrics and Freq. Contrl., Vol. 53, No. 5, pp. 876-879, May 2006.
  12. C. Greenhall and W. Riley, "Uncertainty of Stability Variances Based on Finite Differences", Proc. 35th PTTI Meeting, Dec. 2003.
  13. T.N. Tasset, D.A. Howe and D.B. Percival, "Thêo1 Confidence Intervals", Proc. 2004 Joint FCS/UFFC Meeting, pp. 725-728, Aug. 2004.

 

·      Drift Estimation and Removal

  1. C.A. Greenhall, "Removal of Drift from Frequency Stability Measurements", Telecommunications and Data Acquisition Progress Report 42-65, July-Aug 1981, Jet Propulsion Laboratory, Pasadena, CA, pp. 127-132, 1981. 
  2. J.A. Barnes, "The Measurement of Linear Frequency Drift in Oscillators'', Proc. 15th Annu. PTTI Meeting, pp. 551-582, Dec. 1983.
  3. M.A. Weiss and C. Hackman, "Confidence on the Three-Point Estimator of Frequency Drift", Proc. 24th Annu. PTTI Meeting, pp. 451-460, Dec. 1992.
  4. M.A. Weiss, D.W. Allan and D.A. Howe, "Confidence on the Second Difference Estimation of Frequency Drift'', Proc. 1992 IEEE Freq. Contrl. Symp., pp. 300-305, June 1992.
  5. “Long Term Quartz Oscillator Aging - A New Approach”, The Standard, Hewlett-Packard Co., pp. 4-5, Jan. 1994.
  6. L.A. Breakiron, “A Comparative Study of Clock Rate and Drift Estimation”.
  7. G.Wei, “Estimations of Frequency and its Drift Rate”, IEEE Trans. Instrum. Meas., Vol. 46, No. 1, pp. 79-82, Feb. 1997.
  8. C.A. Greenhall, "A Frequency-Drift Estimator and Its Removal from Modified Allan Variance", Proc. 1997 IEEE Freq. Contrl. Symp., pp. 428-432, June 1997.
  9. F. Vernotte and M. Vincent, “Estimation of the Measurement Uncertainty of Drift Coefficients Versus the Noise Levels", Proc. 12th European Freq. and Time Forum, pp. 222-227, March 1998.

 

·      Noise Identification, Bias Functions and Simulation

  1. J.A. Barnes, "The Generation and Recognition of Flicker Noise", NBS Report 9284, U.S Department of Commerce, National Bureau of Standards, June 1967.
  2. J.A. Barnes, “Effective Stationarity and Power Law Spectral Densities”, NBS Frequency-Time Seminar Preprint, Feb. 1968.
  3. J.A. Barnes, “Tables of Bias Functions, B1 and B2, for Variances Based on Finite Samples of Processes with Power Law Spectral Densities”, NBS Technical Note 375, Jan. 1969.
  4. J.A. Barnes and D.W. Allan, “Recognition and Classification of LF Divergent Noise Processes”, NBS Division 253 Class Notes, circa 1970.
  5. J.A. Barnes, "Models for the Interpretation of Frequency Stability Measurements", NBS Technical Note 683, U.S Department of Commerce, National Bureau of Standards, Aug. 1976.
  6. C.A. Greenhall and J.A. Barnes, "Large Sample Simulation of Flicker Noise", Proc. 19th Annu. PTTI Meeting, pp. 203-217, Dec. 1987 and Proc. 24th Annu. PTTI Meeting, p. 461, Dec. 1992.
  7. N.J. Kasdin and T. Walter, "Discrete Simulation of Power Law Noise", Proc. 1992 IEEE Freq. Contrl. Symp., pp. 274-283, May 1992.
  8. T. Walter, “Characterizing Frequency Stability: A Continuous Power-Law Model with Discrete Sampling”, IEEE Trans. Instrum. Meas., Vol. 43, No. 1, pp. 69-79, Feb. 1994.
  9. S.K. Park and K.W. Miller, "Random Number Generators: Good Ones are Hard to Find'', Comm. ACM, Vol. 31, No. 10, pp. 1192-1201.
  10. D. Howe, R. Beard, C. Greenhall, F. Vernotte and W. Riley, "A Total Estimator of the Hadamard Function Used for GPS Operations", Proc. 32nd PTTI Meeting, pp. 255-268, Nov. 2000.
  11. W.J. Riley and C.A. Greenhall, "Power Law Noise Identification Using the Lag 1 Autocorrelation", Proc. 18th European Freq. and Time Forum, April 2004.
  12. W.J. Riley, "Confidence Intervals and Bias Corrections for the Stable32 Variance Functions", Hamilton Technical Services.

 

·      Dead Time

  1. J.A. Barnes and D.W. Allan, “Variances Based on Data with Dead Time Between the Measurements", NIST Technical Note 1318, U.S. Department of Commerce, National Institute of Standards and Technology, 1990.
  2. D.B Sullivan, D.W Allan, D.A. Howe and F.L. Walls (Editors), "Characterization of Clocks and Oscillators", NIST Technical Note 1337, U.S. Department of Commerce, National Institute of Standards and Technology, TN-296-335, March 1990.
  3. J.A. Barnes, "The Analysis of Frequency and Time Data", Austron, Inc., Dec. 1991.
  4. D.A. Howe and E.E.Hagn, "Limited Live-Time Measurements of Frequency Stability", Proc. Joint FCS/EFTF, pp. 1113-1116, April 1999.
  5. W.J. Riley, "Gaps, Outliers, Dead Time, and Uneven Spacing in Frequency Stability Data”, Hamilton Technical Services.

 

·      3-Cornered Hat

  1. J.E. Gray and D.W. Allan, "A Method for Estimating the Frequency Stability of an Individual Oscillator", Proc. 28th Freq. Contrl. Symp., pp. 243-246, May 1974.
  2. J. Groslambert, D. Fest, M. Oliver and J.J. Gagnepain, "Characterization of Frequency Fluctuations by Crosscorrelations and by Using Three or More Oscillators", Proc..35th Freq. Contrl. Symp., pp. 458-462, May 1981.
  3. S.R. Stein, "Frequency and Time - Their Measurement and Characterization'', Chapter 12, Section 12.1.9, Separating the Variances of the Oscillator and the Reference, pp. 216-217, Precision Frequency Control , Vol. 2, Edited by E.A. Gerber and A. Ballato, Academic Press, New York, 1985, ISBN 0-12-280602-6.
  4. P. Tavella and A. Premoli, "Characterization of Frequency Standard Instability by Estimation of their Covariance Matrix", Proc. 23rd PTTI Meeting, pp. 265-276. Dec. 1991.
  5. P. Tavella and A. Premoli, "A Revisited Tree-Cornered Hat Method for Estimating Frequency Standard Instability", IEEE Trans. Instrum. Meas., IM-42, pp. 7-13, Feb. 1993.
  6. C.R. Ekstrom and P.A. Koppang, "Error Bars for Three-Cornered Hats", IEEE Trans. UFFC, Vol. 53, No. 5, pp. 876-879, May 2006.
  7. W.J. Riley, "Application of the 3-Cornered Hat Method to the Analysis of Frequency Stability", Hamilton Technical Services.

 

·      Domain Conversions

  1. A.R. Chi, “The Mechanics of Translation of Frequency Stability Measures Between Frequency and Time Domain Measurements”, Proc. 9th Annu. PTTI Meeting, pp. 523-548, Dec.1977.
  2. J. Rutman, "Relations Between Spectral Purity and Frequency Stability”, pp. 160-165.
  3. R. Burgoon and M.C. Fisher, “Conversion Between Time and Frequency Domain of Intersection Points of Slopes of Various Noise Processes”, 32th Annu. Symp. on Freq. Contrl., pp.514-519, June 1978.
  4. W.F. Egan, “An Efficient Algorithm to Compute Allan Variance from Spectral Density”, IEEE Trans. Instrum. Meas., Vol. 37, No. 2, pp. 240-244, June 1988.
  5. F. Vernotte, J. Groslambert and J.J. Gagnepain, “Practical Calculation Methods of Spectral Density of Instantaneous Normalized Frequency Deviation from Instantaneous Time Error Samples”, Proc. 5th European Freq. and Time Forum, pp. 449-455, March 1991.
  6. F. Thomson, S. Asmar and K. Oudrhiri, “Limitations on the Use of the Power-Law Form of Sy(f) to Compute Allan Variance”, IEEE Trans. Ultrasonics, Ferroelectrics and Freq. Contrl., Vol. 52, No. 9, pp. 1468-1472, Sept. 2005.
  7. W.J. Riley, "Stable32 Frequency Domain Functions", Hamilton Technical Services.

 

·      Robust Statistics

  1. D.B. Percival, "Use of Robust Statistical Techniques in Time Scale Formation", Preliminary Report, U.S. Naval Observatory Contract No. N70092-82-M-0579, 1982.
  2. Gernot M.R. Winkler, "Introduction to Robust Statistics and Data Filtering", Tutorial at 1993 IEEE Freq. Contrl. Symp., Sessions 3D and 4D, June 1, 1993.
  3. V. Barnett and T. Lewis, Outliers in Statistical Data, 3rd Edition, John Wiley & Sons, Chichester, 1994, ISBN 0-471-93094-6.

 

·      Computation and Algorithms

  1. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes in C, Cambridge Univ. Press, Cambridge, U.K., 1988, pp.216-217.
  2. C.A. Greenhall, "A Shortcut for Computing the Modified Allan Variance'', Proc. 1992 IEEE Freq. Contrl. Symp., pp. 262-264, May 1992.
  3. W.J. Riley, "A Test Suite for the Calculation of Time Domain Frequency Stability", Proc. 1995 IEEE Freq. Contrl. Symp., pp. 360-366, June 1995.
  4. W.J. Riley, "Addendum to a Test Suite for the Calculation of Time Domain Frequency Stability", Proc. 1996 IEEE Freq. Contrl. Symp., pp. 880-882, June 1996.
  5. M. Kasznia, “Some Approach to Computation of ADEV, TDEV and MTIE”, Proc. 11th European Freq. and Time Forum, pp. 544-548, March 1997.

 

·      Measurements

  1. D.W. Allan, "Picosecond Time Difference Measurement System", Proc. 29th Annu. Symp. on Freq. Contrl., pp. 404-411, May 1975.
  2. D.A. Howe, D.W. Allan and J.A. Barnes, "Properties of Signal Sources and Measurement Methods'', Proc. 35th Annu. Symp. on Freq. Contrl., May 1981, pp. 1-47.
  3. S.R. Stein, "Frequency and Time - Their Measurement and Characterization'', Chapter 12, pp.191-416, Precision Frequency Control, Vol. 2, Edited by E.A. Gerber and A. Ballato, Academic Press, New York, 1985, ISBN 0-12-280602-6.
  4. S. Stein, D.Glaze, J. Levine, J. Gray, D. Hilliard, D. Howe and L Erb, "Performance of an Automated High Accuracy Phase Measurement System", Proc. 36th Annu. Freq. Contrl. Symp., June 1982, pp. 314-320.
  5. S.R. Stein and G.A. Gifford, "Software for Two Automated Time Measurement Systems", Proc. 38th Annu. Freq. Contrl. Symp, June 1984, pp. 483-486.
  6. Data Sheet, Model 5110A Time Interval Analyzer, Timing Solutions Corporation (now Symmetricom) 5335 Sterling Dr, Suite B Boulder, CO 80301 USA.
  7. Data Sheet, A7 Frequency & Phase Comparator Measurment System, Quartzlock (UK) Ltd., Gothic, Plymouth Road, Totnes, Devon, TQ9 5LH England.
  8. C.A. Greenhall, "Oscillator-Stability Analyzer Based on a Time-Tag Counter", NASA Tech Briefs, NPO-20749, May 2001, p. 48.
  9. C.A. Greenhall, "Frequency Stability Review", Telecommunications and Data Acquisition Progress Report 42-88, Oct-Dec 1986, Jet Propulsion Laboratory, Pasadena, CA, pp. 200-212, Feb. 1987.

 

 

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