MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity
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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.
KeywordsFourier transform Power spectral density Irregular sampling Maximum entropy data analysis
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- 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
- Durrett, R.: The Essentials of Probability. Duxbury Press, A Division of Wadsworth, Inc., Belmont (1994) Google Scholar
- Henden, A.A.: Observations from the AAVSO International Database (2011) private communication Google Scholar
- 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
- Skilling, J.: In: Skilling, J. (ed.) Maximum Entropy and Bayesian Methods, Cambridge, England, 1988, p. 45. Kluwer Academic, Dordrecht (1989) Google Scholar
- 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
- Wannier, G.H.: Statistical Physics. Wiley, New York (1969) Google Scholar