Astrophysics and Space Science

, Volume 338, Issue 1, pp 35–48 | Cite as

MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity

  • Robert W. JohnsonEmail author
Original Article


The principle of maximum entropy is applied to the spectral analysis of a data signal with general variance matrix and containing gaps in the record. The role of the entropic regularizer is to prevent one from overestimating structure in the spectrum when faced with imperfect data. Several arguments are presented suggesting that the arbitrary prefactor should not be introduced to the entropy term. The introduction of that factor is not required when a continuous Poisson distribution is used for the amplitude coefficients. We compare the formalism for when the variance of the data is known explicitly to that for when the variance is known only to lie in some finite range. The result of including the entropic measure factor is to suggest a spectrum consistent with the variance of the data which has less structure than that given by the forward transform. An application of the methodology to example data is demonstrated.


Fourier transform Power spectral density Irregular sampling Maximum entropy data analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Boyd, J.P.: J. Comput. Phys. 103(2), 243 (1992). doi: 10.1016/0021-9991(92)90399-J MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. Bretthorst, G.L.: Bayesian Spectrum Analysis and Parameter Estimation. Springer, Berlin (1988) zbMATHGoogle Scholar
  3. Bryan, R.: Eur. Biophys. J. 18, 165 (1990). doi: 10.1007/BF02427376 MathSciNetCrossRefGoogle Scholar
  4. Buck, B., Macaulay, V.A.: In: Smith, C.R., Erickson, G.J., Neudorfer, P.O. (eds.) Maximum Entropy and Bayesian Methods, Seattle 1991, p. 241. Kluwer Academic, Dordrecht (1992) Google Scholar
  5. Cenker, C., Feichtinger, H.G., Herrmann, M.: In: Computers and Communications. Conference Proceedings, Tenth Annual International Phoenix Conference on, 1991, p. 483. IEEE Press, New York (1991) CrossRefGoogle Scholar
  6. D’Agostini, G.: ArXiv Physics e-prints. In: Bayesian Statistics 6: Proceedings of the Sixth Valencia International Meeting. Oxford Science Publications, Oxford (1998). arXiv:physics/9811045 Google Scholar
  7. Durrett, R.: The Essentials of Probability. Duxbury Press, A Division of Wadsworth, Inc., Belmont (1994) Google Scholar
  8. Gregory, P.: Bayesian Logical Data Analysis for the Physical Sciences. Cambridge University Press, New York (2005) zbMATHCrossRefGoogle Scholar
  9. Henden, A.A.: Observations from the AAVSO International Database (2011) private communication Google Scholar
  10. Johnson, R.W.: Extended Wavelet Transform for Discretely Sampled Data, Chap. 6. In: del Valle, M., noz Guerrero, R.M., Salgado, J.M.G. (eds.) Wavelets: Classification, Theory and Applications, p. 125. Nova Science, Hauppauge (2012). ISBN: 978-1-62100-252-9 Google Scholar
  11. Lomb, N.R.: Astrophys. Space Sci. 39, 447 (1976). doi: 10.1007/BF00648343 ADSCrossRefGoogle Scholar
  12. MacKay, D.J.C.: Neural Comput. 11(5), 1035 (1999) CrossRefGoogle Scholar
  13. Malik, W.Q., Khan, H.A., Edwards, D.J., Stevens, C.J.: In: Advances in Wired and Wireless Communication, 2005 IEEE/Sarnoff Symposium on, p. 125. IEEE Press, New York (2005) CrossRefGoogle Scholar
  14. Marsaglia, G.: Comput. Math. Appl. 12(5–6, Part 2), 1187 (1986). doi: 10.1016/0898-1221(86)90242-7 zbMATHCrossRefGoogle Scholar
  15. Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C, 2nd edn. Cambridge University Press, Cambridge (1992) zbMATHGoogle Scholar
  16. Scargle, J.D.: Astrophys. J. 263, 835 (1982). doi: 10.1086/160554 ADSCrossRefGoogle Scholar
  17. Sivia, D.S.: Data Analysis: A Bayesian Tutorial. Oxford Science Publications. Oxford University Press, Oxford (1996) zbMATHGoogle Scholar
  18. Skilling, J.: In: Skilling, J. (ed.) Maximum Entropy and Bayesian Methods, Cambridge, England, 1988, p. 45. Kluwer Academic, Dordrecht (1989) Google Scholar
  19. Strauss, C., Wolpert, D., Wolf, D.: In: Mohammad-Djafari, A., Demoments, G. (eds.) Maximum Entropy and Bayesian Methods, Paris 1992, p. 113. Kluwer Academic, Dordrecht (1993) Google Scholar
  20. Wannier, G.H.: Statistical Physics. Wiley, New York (1969) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Alphawave ResearchAtlantaUSA

Personalised recommendations