Application of Wavelet-Based Higher-Order Spectra to Detect Short-Time Duration Nonlinear Interactions

Prof. Edward J. Powers

Department of Electrical and Computer Engineering
University of Texas at Austin

Friday, January 18th, 3:00 PM, ENS 637

ejpowers@mail.utexas.edu

Abstract

Fourier-based higher-order spectra (HOS) have proven to be very powerful in detecting and quantifying evidence of nonlinearities in time series data collected from a wide variety of physical systems. Such higher-order spectra have also proven extremely useful in modeling nonlinear physical systems given experimental time series data characterizing excitation and response.

Fourier transform-based HOS provide no time resolution and thus are of no value in detecting short-time duration nonlinear events in an experimental time series. An example of such an event is the occurrence of "extreme" (very large amplitude) waves in the ocean that appear to be associated with a short-time duration phase locking of first-order and higher-order (second- and third-order) wave components.

In this presentation, we demonstrate how the use of (continuous) wavelet transformed-based HOS is capable of detecting short-lived nonlinear events in a time series. This capability will be demonstrated with ocean wave experimental time series data.

Additional confirmation of the wavelet-based HOS approach will be provided through the use of nonlinear (Volterra) digital filters to decompose the wave time series into its respective first-, second-, and third-order components. Such decomposition enables visualization of the short-term phase-locking in the time domain, thereby confirming the wavelet-based HOS results.

Biography

Dr Powers is the Texas Atomic Energy Research Foundation Professor in Engineering and has had several years experience utilizing higher-order statistical signal processing to provide new physical insight into nonlinear wave and turbulence phenomena in continuous media such as fluids and plasmas.

A list of Telecommunications and Signal Processing Seminars is available at from the ECE department Web pages under "Seminars". The Web address for the Telecommunications and Signal Processing Seminars is http://signal.ece.utexas.edu/seminars