Phase Derivatives and Their Applications in Monogenic Signals
Speaker:Prof. Yan Yang
School of Mathematics and Computational Science
Sun Yat-sen University
Date & Time:2 Nov 2012 (Friday) 15:00
Venue:JG06
Organized by:Department of Mathematics

Abstract

In the Clifford algebra setting of Euclidean spaces a monogenic (analytic) signal is naturally defined to be the boundary limit of a monogenic (analytic) function in the related domain. In an earlier paper we defined a scalar-valued phase derivative as a candidate of instantaneous frequency of multivariate signals. In this paper by using the scalar-valued phase derivative we obtain fundamental results to connect this phase derivative with the Fourier frequency. The results generalize the latest results of quadrature phase derivative in one dimension to multi-dimensional cases in the Clifford algebra setting. We also prove two uncertainty principles in higher dimensions of which one is for scalar-valued and the other is for Clifford-valued signals but of the axial form.

Biography

Prof. Yan Yang is currently the Associate Professor of School of Mathematics and Computational Science at Sun Yat-Sen University. Prof. Yang obtained her Ph.D. at University of Macau. She was awarded Excellent Teachers Award by International Business School of Sun Yat-Sen University in 2008. Prof. Yang is interested in Complex Variables, Harmonic Analysis, Value Distribution and Clifford Analysis. Her recent publications include, On the precision order and the Type-function of the Laplace-Steltjes transform, Hardy-Sobolev derivatives of phase and amplitude, and their applications, Phase derivative of Monogenic signals in higher dimensional spaces, Zeroes of Slice monogenic functions and Zero-sets of Clifford analysis functions with real coefficients.