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.
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References
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© 1988 Kluwer Academic Publishers
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Bretthorst, G.L. (1988). Excerpts from Bayesian Spectrum Analysis and Parameter Estimation. In: Erickson, G.J., Smith, C.R. (eds) Maximum-Entropy and Bayesian Methods in Science and Engineering. Fundamental Theories of Physics, vol 31-32. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3049-0_5
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DOI: https://doi.org/10.1007/978-94-009-3049-0_5
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