**References for Frequency Stability Analysis**

· Notes

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

· General

- Special Issue on
Frequency Stability
*, Proc. IEEE*, Vol. 54, Feb. 1966. *Proc. IEEE*, Vol. 55, June 1967.- J.A. Barnes, “Atomic Timekeeping and the Statistics of
Precision Signal Generators,”
*IEEE Proceedings*, vol. 54, pp. 207-219, 1966. - J.A. Barnes, et. al., “Characterization of Frequency
Stability”,
*IEEE Trans. Instrum. Meas*., Vol. IM-20, No. 2, pp. 105-120, May 1971. - B.E. Blair (Editor), "Time and Frequency: Theory and Fundamentals",
*NBS Monograph 140*, U.S. Department of Commerce, National Bureau of Standards, May 1974. - G. Winkler, "A Brief Review of Frequency Stability Measures",
*Proc. 8th PTTI Meeting*, pp. 489-527, Dec. 1976. - J. Rutman, "Oscillator
Specifications: A Review of Classical and New Ideas",
*Proc. 31th Annu. Symp. on Freq. Contrl*., pp.291-310, June 1977. - J. Vanier and M. Tetu, "Time Domain
Measurement of Frequency Stability",
*Proc. 10th PTTI Meeting*, pp. 247-291, Nov. 1978. - P.Lesage and C. Audoin, “Characterization and Measurement of
Time and Frequency Stability”,
*Radio Science*, Vol. 14, No. 4, pp. 521-539, 1979. - 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. - 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. - 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. *Proc. IEEE*, Vol. 74, Jan. 1986.- 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. - 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. - D.W. Allan, et al., "Standard
Terminology for Fundamental Frequency and Time Metrology",
*Proc. 42nd Annu. Freq. Control Symp.*, pp. 419-425, June, 1988. - 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. - D.W. Allan, “Characterization of Precision Clocks and Oscillators”, Class Notes, NRL Workshop, Nov. 1990.
- D.W. Allan, "Time and Frequency Metrology: Current Status and
Future Considerations'',
*Proc. 5th European Freq. and Time Forum*, pp. 1-9, March 1991. - Special Issue on Time and
Frequency
*, Proc. IEEE*, Vol. 79, July 1991. - J. Rutman and F. L. Walls, "Characterization
of Frequency Stability in Precision Frequency Sources"
*, Proc. IEEE*, Vol. 79, July 1991. - J.A. Barnes, "The Analysis of Frequency and Time Data", Austron, Inc., Dec. 1991.
- 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. - C. Audoin and B. Guinot,
*The Measurement of Time*, Cambridge University Press, 2001. - G.E.P. Box and G.M. Jenkins,
*Time Series Analysis: Forecasting and Control*, San Francisco: Holden-Day, 1970. - W.J. Riley, "The Basics of Frequency Stability Analysis", Hamilton Technical Services.
- W.J. Riley, "The Calculation of Time Domain Frequency Stability”, Hamilton Technical Services.
- W.J. Riley, “Techniques for Frequency Stability Analysis”, Tutorial at the 2003 Intl. Freq. Cont. Symp., May 2003.

· Standards and Specifications

- "Characterization of Frequency and
Phase Noise",
*Report 580*, - MIL-PRF-55310, Oscillators, Crystal, General Specification For.
*ITU-R Handbook*, 1995*.**Guide to the Expression of Uncertainty in Measurement*, International Standards Organization, 1995, ISBN 92-67-10188-9.- "IEEE
Standard Definitions of Physical Quantities for Fundamental Frequency and Time
Metrology - Random Instabilities",
*IEEE Std 1139-1999*, July 1999.

· Classic (Pre-Allan variance)

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

· Allan Variance

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

· Modified Allan Variance

- 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. - 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. - C.A.
Greenhall, "Estimating
the Modified Allan Variance",
*Proc. 1995 IEEE Freq. Contrl. Symp*., pp. 346-353, May 1995. - 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. - 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

- D.W. Allan and H. Hellwig, “Time Deviation and Time Prediction Error for Clock Specification, Characterization, and Application”, March 1981.
- 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. - 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

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

· Modified Hadamard Variance

- 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.
- 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

- 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. - 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. - D.A. Howe and
K.J. Lainson, "Effect
of Drift on TOTALDEV",
*Proc. 1996 Intl. Freq. Cont. Symp*. , pp. 883-889, June 1996 - 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. - 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. - D.B. Percival
and D.A. Howe, "Total Variance as
an Exact Analysis of the Sample Variance",
*Proc. 1997 PTTI Meeting*, Dec. 1997. - 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. - 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. - 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. - 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

- 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

- 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

- 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.
- D.A. Howe and T.N. Tasset, "Thê01: Characterization of Very Long-Term Frequency Stability", Proc. 2004 EFTF .
- D.A. Howe, "ThêoH: A Hybrid, High-Confidence Statistic that Improves on the Allan Deviation", Metrologia 43 (2006), S322-S331.
- 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

- 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. - 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. - Bregni, " Clock
Stability Characterization and Measurement in Telecommunications”,
*IEEE Trans. Instrum. Meas*., Vol. IM-46, No. 6, pp. 1284-1294, Dec. 1997. - 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. - G. Zampetti,
“Synopsis
of Timing Measurement Techniques Used in Telecommunucations”,
*Proc. 24th PTTI Meeting*, pp. 313-326, Dec. 1992. - M.J. Ivens, "Simulating the Wander Accumulation in a SDH Synchronisation Network", Master's Thesis, University College, London, UK, November 1997.
- 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

- 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. - 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. - 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. - 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. - T. Walter,
"A
Multi-Variance Analysis in the Time Domain",
*Proc. 24th PTTI Meeting*, pp. 413-424, Dec. 1992.

· Dynamic Stability

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

· Confidence Intervals

- 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. - 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. - 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. - 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. - 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. - W.J. Riley, “Confidence Intervals and Bias Corrections for the Stable32 Variance Functions”, Hamilton Technical Services, 2000.
- 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.
- 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. - 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. - 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. - 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. - C. Greenhall and W. Riley, "Uncertainty of Stability Variances Based on Finite Differences", Proc. 35th PTTI Meeting, Dec. 2003.
- 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

- 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. - J.A. Barnes, "The Measurement of Linear Frequency Drift in
Oscillators'',
*Proc. 15th Annu. PTTI Meeting*, pp. 551-582, Dec. 1983. - 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. - 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. - “Long Term Quartz Oscillator Aging - A New Approach”,
*The Standard*, Hewlett-Packard Co., pp. 4-5, Jan. 1994. - L.A. Breakiron, “A Comparative Study of Clock Rate and Drift Estimation”.
- G.Wei, “Estimations of Frequency and its Drift Rate”,
*IEEE Trans. Instrum. Meas*., Vol. 46, No. 1, pp. 79-82, Feb. 1997. - 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. - 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

- J.A. Barnes, "The Generation and Recognition of Flicker Noise",
*NBS Report 9284*, U.S Department of Commerce, National Bureau of Standards, June 1967. - J.A. Barnes, “Effective Stationarity and Power Law Spectral Densities”, NBS Frequency-Time Seminar Preprint, Feb. 1968.
- J.A. Barnes, “Tables of Bias Functions, B
_{1}and B_{2}, for Variances Based on Finite Samples of Processes with Power Law Spectral Densities”,*NBS Technical Note 375*, Jan. 1969. - J.A. Barnes and D.W. Allan, “Recognition and Classification of LF Divergent Noise Processes”, NBS Division 253 Class Notes, circa 1970.
- 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. - 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. - N.J. Kasdin and T. Walter, "Discrete
Simulation of Power Law Noise",
*Proc. 1992 IEEE Freq. Contrl. Symp.*, pp. 274-283, May 1992. - 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. - 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. - 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.
- 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.
- W.J. Riley, "Confidence Intervals and Bias Corrections for the Stable32 Variance Functions", Hamilton Technical Services.

· Dead Time

- 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.
- 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.
- J.A. Barnes, "The Analysis of Frequency and Time Data", Austron, Inc., Dec. 1991.
- D.A. Howe and E.E.Hagn, "Limited Live-Time Measurements of Frequency Stability", Proc. Joint FCS/EFTF, pp. 1113-1116, April 1999.
- W.J. Riley, "Gaps, Outliers, Dead Time, and Uneven Spacing in Frequency Stability Data”, Hamilton Technical Services.

· 3-Cornered Hat

- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- W.J. Riley, "Application of the 3-Cornered Hat Method to the Analysis of Frequency Stability", Hamilton Technical Services.

· Domain Conversions

- 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. - J. Rutman, "Relations Between Spectral Purity and Frequency Stability”, pp. 160-165.
- 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. - 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. - 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. - 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. - W.J. Riley, "Stable32 Frequency Domain Functions", Hamilton Technical Services.

· Robust Statistics

- 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.
- 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.
- V. Barnett and T. Lewis,
*Outliers in Statistical Data*, 3^{rd}Edition, John Wiley & Sons, Chichester, 1994, ISBN 0-471-93094-6.

· Computation and Algorithms

- 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. - C.A. Greenhall, "A
Shortcut for Computing the Modified Allan Variance'',
*Proc. 1992 IEEE Freq. Contrl. Symp*., pp. 262-264, May 1992. - 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. - 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. - M. Kasznia, “Some Approach to Computation of ADEV, TDEV and
MTIE”,
*Proc. 11th European Freq. and Time Forum*, pp. 544-548, March 1997.

· Measurements

- D.W. Allan, "Picosecond
Time Difference Measurement System",
*Proc. 29th Annu. Symp. on Freq. Contrl.*, pp. 404-411, May 1975. - 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. - S.R. Stein, "Frequency
and Time - Their Measurement and Characterization'', Chapter 12,
pp.191-416,
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