MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity |
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| Authors: | Robert W Johnson |
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| Institution: | (1) Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, 240 Longwood Avenue, Boston, MA 02115, USA; |
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| Abstract: | 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. |
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