Title:
Blindsource signal decomposition according to a general mathematical model
Abstract:
The problems of function factorization and decomposition of
functions from certain function spaces have a long history in mathematical
development, and play an important role to the recent progress in computational
harmonic analysis. However, for realworld applications, particularly in this "big
data" era, functions of interest are usually not welldefined, but perhaps
governed by some nonlinear function models. In this presentation, we will focus
on functions that represent realworld signals and their unknown subsignals. In
general, such functions can be considered as the real parts of certain
exponential sums, but usually with nonlinear amplitudes and phases. We will
discuss the background and motivation of the socalled adaptive harmonic
model and present some main ideas and computational procedures, along with
a selection of recent mathematical results, on the recovery of the unknown sub
signals of any reasonably wellbehaved blindsource, via extraction of their
instantaneous frequencies from discrete samples of the blindsource signal.
Demonstrative examples will be presented to facilitate our discussion.
