Applications of DSP to Nonlinear Physical Phenomena
Dr. Edward J. Powers
Dept. of Electrical and Computer Engineering,
The University of Texas at Austin
Austin, Texas
Friday, September 25, 1998, ENS 302
In this presentation we will consider applications of higher-order statistical signal processing and Volterra filters in analyzing, interpreting, and modeling time series data characteristic of a variety of nonlinear physical phenomena. The Volterra series provides a systematic framework within which to model time series data from nonlinear physical ( as well as numerical) experiments. We will focus on the challenges and subtleties involved in estimating the frequency-domain Volterra kernels ( i.e., linear, quadratic, and cubic Volterra transfer functions) via higher-order spectral analysis of the experimentally observed excitation-response time series data. Correct knowledge of the Volterra frequency-domain transfer functions is essential, since such knowledge allows one to: (1) quantify the strength of various nonlinear interactions, (2) determine related physics-based quantities such as three-wave and four-wave coupling coefficients, (3) quantify the rate of nonlinear energy transfer between interacting frequency ( and wavenumber) components, (4) decompose an experimentally observed response power spectrum into its constituent linear, quadratic, and cubic components as a function of frequency, and (5) compensate for such nonlinearities where desirable. These and other issues will be addressed with the aid of physical experimental data characteristic of nonlinear wave interactions and nonlinear fluid-structure interactions.