Student Brown Bag Seminar

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, with examples. I then describe how the variance reduction method of control variates can be applied to power spectrum estimation. A comparison of these tools on spectral estimation and some related tasks, including spectral factorization and whitening is presented. Time permitting, I apply the techniques to the Kuramoto-Sivashinsky equation, a prototypical model of spatiotemporal chaos.

Place:               Math, 402 and Zoom: Link https://arizona.zoom.us/j/83541348598  Password:  BB2022