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A Bayesian Curve Fitting Approach to Power Spectrum Estimation

A Bayesian method of estimating the power spectra of stationary random processes is proposed. Initially we estimate the true spectra via the log periodogram but due to the inadequacies of the periodogram when the true spectrum has a high dynamic range and/or is rapidly varying we find that improved results can be obtained using multitaper spectrum estimates (Percival and Walden, 1993). We follow the method of Denison, Mallick and Smith (1998) and estimate the spectra using piecewise polynomials with random knot locations. The methodology is shown, using simulated examples, to be successful in giving "smooth" estimates which also capture peaks and troughs in the true spectra.