Nonlinear Systems exhibiting chaotic behavior can be considered as a source of a great variety of signals. Given a time series measured from a known or an unknown dynamical system we address a series of problems, such as section-wise approximation of the measured signal by pieces of trajectories from a chosen nonlinear dynamical system (model); signal restoration when the measured signal has been corrupted e.g. by quantization; signal coding and compression. The key to attack these problems is estimation of the initial conditions for a dynamical system which is used as the generator of approximating waveforms.
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