Analysis of Multivariate Nonstationary Time Series Using the Localized Fourier Library

Hernando Ombao*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Using the SLEX library as the primary tool, we develop a systematic, flexible, and computationally efficient procedure for analyzing multivariate nonstationary time series. The SLEX library is a collection of bases; each of which consists of localized Fourier waveforms. In the problem of signal representation and spectral estimation, one can select, from the set of bases in the SLEX library, the one that best represents the underlying process. Moreover, in discrimination and classification of nonstationary time series, one can select the basis that gives the maximal separation between classes of nonstationary time series. We illustrate the SLEX methods by analyzing multichannel EEGs recorded during an epileptic seizure and during a visual-motor experiment.

Original languageEnglish (US)
Title of host publicationHandbook of Statistics
PublisherElsevier B.V.
Number of pages30
StatePublished - Jan 1 2012

Publication series

NameHandbook of Statistics
ISSN (Print)0169-7161


  • Coherence
  • Discrimination
  • Fourier transform
  • Nonstationary time series
  • Smooth localized complex exponentials
  • Spectral analysis
  • Spectral matrix

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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