Dynamical Theory Formalism for Robust Modeling of Damped, Undamped, and Nonlinear Oscillatory Signals

The paper explores a novel framework for signal representation based on dynamic information in a signal that is well suited for robust analysis of low SNR signals and extraction of time-varying features. The method is derived from dynamical theory but formulated in a basic parameter estimation paradigm. Modeling the changes in data provides a compact depiction of time-variant and invariant information plus features related to data dynamics. The method also provides strong noise mitigation properties even when noise statistics is poorly understood. The signal processing formulation supplies a connection between the time-delay and the Fourier domains. This connection helps us bridge non-linear dynamical and signal processing theories and brings a powerful novel tool to signal analysis at large. The experiment is presented using a speech sample from the TIMIT database.