User menu

Accès à distance ? S'identifier sur le proxy UCLouvain | Saint-Louis

A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 1: Frequency analysis

  • Open access
  • PDF
  • 6.68 M
  1. Akaike H., A new look at the statistical model identification, 10.1109/tac.1974.1100705
  2. Bretthorst G. Larry, Nonuniform sampling: Bandwidth and aliasing, 10.1063/1.1381847
  3. Brockwell Peter J., Davis Richard A., Time Series: Theory and Methods, ISBN:9781441903198, 10.1007/978-1-4419-0320-4
  4. Brockwell Peter J., Davis Richard A., Introduction to Time Series and Forecasting, ISBN:9783319298528, 10.1007/978-3-319-29854-2
  5. Bronez T.P., Spectral estimation of irregularly sampled multidimensional processes by generalized prolate spheroidal sequences, 10.1109/29.9031
  6. Ferraz-Mello S., Estimation of Periods from Unequally Spaced Observations, 10.1086/112924
  7. Stark P.B., Fodor I.K., Multitaper spectrum estimation for time series with gaps, 10.1109/78.887039
  8. Ghil M., Advanced spectral methods for climatic time series, 10.1029/2000rg000092
  9. Harris F.J., On the use of windows for harmonic analysis with the discrete Fourier transform, 10.1109/proc.1978.10837
  10. Hasselmann K., Stochastic climate models Part I. Theory, 10.1111/j.2153-3490.1976.tb00696.x
  11. Heck, A., Manfroid, J., and Mersch, G.: On period determination methods, Astron. Astrophys. Sup., 59, 63–72, 1985.
  12. Jeffreys H., An Invariant Form for the Prior Probability in Estimation Problems, 10.1098/rspa.1946.0056
  13. Jian Zhimin, Zhao Quanhong, Cheng Xinrong, Wang Jiliang, Wang Pinxian, Su Xin, Pliocene–Pleistocene stable isotope and paleoceanographic changes in the northern South China Sea, 10.1016/s0031-0182(03)00259-1
  14. JONES RICHARD H., ACKERSON LYNN M., Serial correlation in unequally spaced longitudinal data, 10.1093/biomet/77.4.721
  15. Kelly Brandon C., Becker Andrew C., Sobolewska Malgosia, Siemiginowska Aneta, Uttley Phil, FLEXIBLE AND SCALABLE METHODS FOR QUANTIFYING STOCHASTIC VARIABILITY IN THE ERA OF MASSIVE TIME-DOMAIN ASTRONOMICAL DATA SETS, 10.1088/0004-637x/788/1/33
  16. Kemp David B., Optimizing significance testing of astronomical forcing in cyclostratigraphy : Testing of Astronomical Forcing, 10.1002/2016pa002963
  17. Lenoir, G.: Time-frequency analysis of regularly and irregularly sampled time series: Projection and multitaper methods, PhD thesis, Université catholique de Louvain – Faculté des Sciences – Georges Lemaître Centre for Earth and Climate Research, Louvain-la-Neuve, Belgium, available at: (last access: 22 February 2018), 2017.
  18. Lenoir Guillaume, Crucifix Michel, A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis, 10.5194/npg-25-175-2018
  19. Lomb N. R., Least-squares frequency analysis of unequally spaced data, 10.1007/bf00648343
  20. Mortier A., Faria J. P., Correia C. M., Santerne A., Santos N. C., BGLS: A Bayesian formalism for the generalised Lomb-Scargle periodogram, 10.1051/0004-6361/201424908
  21. Mudelsee, M.: Climate Time Series Analysis – Classical Statistical and Bootstrap Methods, in: Atmospheric and Oceanographic Sciences Library, vol. 42, Springer, Dordrecht, the Netherlands, 2010.
  22. Mudelsee M., Scholz D., Röthlisberger R., Fleitmann D., Mangini A., Wolff E. W., Climate spectrum estimation in the presence of timescale errors, 10.5194/npg-16-43-2009
  23. Pardo-Igúzquiza Eulogio, Rodríguez-Tovar Francisco J., Spectral and cross-spectral analysis of uneven time series with the smoothed Lomb–Scargle periodogram and Monte Carlo evaluation of statistical significance, 10.1016/j.cageo.2012.06.018
  24. Priestley, M.: Spectral Analysis and Time Series, Two Volumes Set, Probability and Mathematical Statistics – A series of Monographs and Textbooks, Third edn., Academic Press, London, UK, San Diego, USA, 1981.
  25. Provost, S.: Moment-Based Density Approximants, The Mathematica Journal, 9, 727–756, available at: (last access: 22 February 2018), 2005.
  26. Provost Serge B., Ha Hyung-Tae, Sanjel Deepak, On approximating the distribution of indefinite quadratic forms, 10.1080/02331880902732123
  27. Rehfeld K., Marwan N., Heitzig J., Kurths J., Comparison of correlation analysis techniques for irregularly sampled time series, 10.5194/npg-18-389-2011
  28. Riedel K.S., Sidorenko A., Minimum bias multiple taper spectral estimation, 10.1109/78.365298
  29. Robinson P.M., Estimation of a time series model from unequally spaced data, 10.1016/0304-4149(77)90013-8
  30. Scargle J. D., Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data, 10.1086/160554
  31. Schulz Michael, Mudelsee Manfred, REDFIT: estimating red-noise spectra directly from unevenly spaced paleoclimatic time series, 10.1016/s0098-3004(01)00044-9
  32. Schulz Michael, Stattegger Karl, Spectrum: spectral analysis of unevenly spaced paleoclimatic time series, 10.1016/s0098-3004(97)00087-3
  33. Stacy E. W., Mihram G. A., Parameter Estimation for a Generalized Gamma Distribution, 10.1080/00401706.1965.10490268
  34. Thomson D.J., Spectrum estimation and harmonic analysis, 10.1109/proc.1982.12433
  35. Torrence, C. and Compo, G.: A Practical Guide to Wavelet Analysis, B. Am. Meteorol. Soc., 79, 61–78,<0061:APGTWA>2.0.CO;2, 1998.
  36. Torrésani, B.: Analyse continue par ondelettes, Savoirs actuels/Série physique, CNRS Editions and EDP Sciences, Paris, France, 1995.
  37. Uhlenbeck G. E., Ornstein L. S., On the Theory of the Brownian Motion, 10.1103/physrev.36.823
  38. Vio R., Andreani P., Biggs A., Unevenly-sampled signals: a general formalism for the Lomb-Scargle periodogram, 10.1051/0004-6361/201014079
  39. Walden A. T., A unified view of multitaper multivariate spectral estimation, 10.1093/biomet/87.4.767
  40. Welch P., The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms, 10.1109/tau.1967.1161901
  41. Zechmeister M., Kürster M., The generalised Lomb-Scargle periodogram : A new formalism for the floating-mean and Keplerian periodograms, 10.1051/0004-6361:200811296
Bibliographic reference Lenoir, Guillaume ; Crucifix, Michel. A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 1: Frequency analysis. In: Nonlinear Processes in Geophysics, Vol. 25, no.1, p. 145-173 (2018)
Permanent URL