Graduate School and Research Center in Digital Sciences

Seminar: DS Talk

Philip De Leon

Digital Security

Date: February 18, 2016

Location: Eurecom - Salle Fourier

Title: Theory of the Hilbert Spectrum Speaker: Philip De Leon Summary In this talk, we describe our research into the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor’s complex extension and re-evaluate fundamental principles of time-frequency analysis. We provide a multicomponent model of a signal that enables rigorous definition of instantaneous frequency on a per-component basis. Within our framework, we have shifted all uncertainty of the latent signal to its quadrature. In this approach, uncertainty is not a fundamental limitation of analysis, but rather a manifestation of the limited view of the observer. With the appropriate assumptions made on the signal model, the instantaneous amplitude and instantaneous frequency can be obtained exactly, hence exact representation of a signal in the coordinates of time and frequency can be achieved. However, uncertainty now arises in obtaining the correct assumptions, i.e. how to correctly choose the quadrature of the components. Speaker biography: Phillip De Leon received the B.S. Electrical Engineering and the B.A. in Mathematics from the University of Texas at Austin. He was awarded the AT&T Bell Laboratories Cooperative Research Doctoral Fellowship and received the M.S. and Ph.D. degrees in Electrical Engineering from the University of Colorado at Boulder. He holds the Paul W. and Valerie Klipsch Distinguished Professorship in the Klipsch School of Electrical and Computer Engineering at New Mexico State University and is the Director of the Advanced Speech and Audio Processing Laboratory. He is currently on research sabbatical and will be spending two months (February and March) at EURECOMM. This is his first time visiting France.

DS Talk