Excerpts from Bayesian Spectrum Analysis and Parameter Estimation

Abstract

Bayesian spectrum analysis is still in its infancy. I t w as born when E. T. Jaynes derived the periodogram m2 as a suucient 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 end substantial improvements in resolution over Fourier transform methods.