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A comparison of spectral estimation methods
Estimating power spectra is frequently a first step in the analysis of stationary time series generated by chaotic and/or stochastic dynamical systems. Accurate estimates are needed for, e.g., data driven modeling and model reduction. Common challenges include the presence of multiple timescales and slow decay of correlations, and when the range of the power spectrum is large. In this talk, I review the definition of the power spectrum of a stationary stochastic process as well as some estimation techniques. Spectral factorization and modeling and whitening filters are also briefly discussed. I then present a new method for spectral estimation which involves the iterative whitening of data. A comparison of these tools on spectral estimation is presented. I also apply these techniques to the Kuramoto-Sivashinsky equation, a prototypical model of spatiotemporal chaos.
Math, 402 and Zoom https://arizona.zoom.us/j/83758253931Password: applied