Adaptive Fourier Series in Signal Decomposition: (I) Fundamental Theory; (II) Algorithm
Speaker:Prof. Qian Tao
Professor and Head of Department of Mathematics
Faculty of Science and Technology
University of Macau
Date & Time:03 Dec 2009 (Thursday) 10:00 - 12:00


Decomposition of signals into basic ones with meaningful analytic instantaneous frequencies is fundamental in signal analysis and harmonic analysis. Series expansional in the Fourier basis, Laguerre basis and the "two-parameter Kautz" basis all belong to this category. We propose a decomposition model in this category with fast convergence in terms of energy. The proposed approximation is called adaptive rational function or adaptive Takenaka-Malmquist (TM) approximation. The adaptive decomposition falls outside the scope of the traditional study of rational or Takenaka systems. The key point of the new approach is that the zeros that define the system are adaptively chosen according to the function to be decomposed. As result, the obtained system may not be a basis of the space of the physically realizable signals. It, however, gives rise to a fast decomposition of the given signal into their intrinsic constructive components possessing non-negative analytic instantaneous frequencies.