Signal decomposition for nonstationary processes

The main purpose of this dissertation is to explore and develop better signal modeling (decomposition) methods for nonstationary and/or nonlinear dynamic processes. Localization is the main focus. The characteristics of a nonstationary or nonlinear signal are decomposed onto a set of basis functions, either in the phase space spanned by time-frequency coordinates as Gabor proposed, or in the phase space spanned by a set of derivatives of different degree as defined in physics.

To deal with time-varying signals, a Multiresolution Parametric Spectral Estimator (MPSE) is proposed together with its theory, techniques and applications. The resolution study provides the characteristics of windowed Fourier transforms, wavelet transforms, fixed resolution parametric spectral estimators, and the newly developed MPSE. Both the theoretical and the experimental results show that, of the above techniques, MPSE is the best in resolution. Furthermore, with proper a priori knowledge, MPSE can yield better resolution than the lower bound defined by the Heisenberg uncertainty principle. The application examples demonstrate the great potential of the MPSE method for tracking and analyzing time-varying processes.

To deal with the time-varying characteristics caused by linearization of nonlinear processes, the Radial Basis Function Network (RBFN) is proposed for modeling nonlinear processes from a 'local' to a 'global' level. An equal distance sample rule is proposed for constructing the RBEN. Experiments indicate that the RBFN is a promising method for modeling deterministic chaos as well as stochastic processes, be it linear or nonlinear. The 'local' to 'global' approach of the RBEN also provides great potential for structure adaptation and knowledge accumulation.