Ecole d'ingénieur et centre de recherche en Sciences du numérique

Seminar: The Hilbert Spectrum: A General Framework for Time-Frequency Analysis

Philippe DELEON - Professeur

Date: 7 novembre 2017

Lieu: Eurecom - TURING

Abstract: This talk will review our research into the old problem of representing a signal in the coordinates of time and frequency. We review the fundamental Hilbert transform relation in systems analysis and argue that the dual relation assumed in signal analysis, i.e. spectral single-sidedness is not necessarily justifiable. Therefore, we abandon the analytic signal and define a signal model composed of a superposition of complex, AM– FM components that enables rigorous definition of instantaneous amplitude and instantaneous frequency. Based on this model, we introduce the Hilbert Spectrum (HS) as the ideal instantaneous spectrum, which specializes to the Fourier spectrum. Numerical algorithms are given for computing a HS where the component is assumed to be an latent intrinsic mode function. Examples using the proposed algorithms are provided that show the HS simultaneously exhibits fine resolution in both the coordinates of time and frequency simultaneously. Bio: Phillip De Leon received the B.S. Electrical Engineering and the B.A. in Mathematics from the University of Texas at Austin, in 1989 and 1990 respectively and the M.S. and Ph.D. degrees in Electrical Engineering from the University of Colorado at Boulder, in 1992 and 1995 respectively. In 2016, he spent part of his sabbatical at EURECOM. He currently holds the Klipsch Distinguished Professorship in Electrical and Computer Engineering at New Mexico State University (NMSU) and serves as the Associate Dean of Research. He has co-authored over 70 refereed papers in international journals and conferences. His research interests include machine learning, speaker recognition, speech processing, and time-frequency analysis.

Université New Mexico California

The Hilbert Spectrum: A General Framework for Time-Frequency Analysis

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