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Excerpts from Bayesian Spectrum Analysis and Parameter Estimation

  • G. Larry Bretthorst
Part of the Fundamental Theories of Physics book series (FTPH, volume 31-32)

Abstract

Bayesian spectrum analysis is still in its infancy. It was born when E. T. Jaynes derived the periodogram2 as a sufficient statistic for determining the spectrum of a time sampled data set containing a single stationary frequency. Here we extend that analysis and explicitly calculate the joint posterior probability that multiple frequencies are present, independent of their amplitude and phase, and the noise level. This is then generalized to include other parameters such as decay and chirp. Results are given for computer simulated data and for real data ranging from magnetic resonance to astronomy to economic cycles. We find substantial improvements in resolution over Fourier transform methods.

Keywords

Power Spectral Density Discrete Fourier Transform Sunspot Number Harmonic Frequency Nuisance Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • G. Larry Bretthorst
    • 1
  1. 1.Department of PhysicsWashington UniversitySt. LouisUSA

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