Approximation and compression of arbitrary time-series based on nonlinear dynamics

Given a measured output signal from a nonlinear deterministic process in the form of a time series we estimate initial conditions in successive time intervals which reproduce in an optimal way sections of the output signal. Thus, the measured signal can be coded in terms of model equations, its parameters and a set of initial conditions. We achieve signal approximation and compression at the same time. We discuss continuous-time and discrete-time approaches