Chaotic evolution and nonlinear prediction in signal separation applications

by William W. Taylor

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Certain physically generated signal separation problems can be reformulated as deterministic nonlinear prediction problems with a quantifiable prediction accuracy despite their apparent random behavior. This provides an alternate signal processing methodology for these problems. The randomness is accounted for in this method by chaotic dynamics in the systems which generate and contaminate the signal of interest. This induces an invariant probability measure supported on a chaotic attractor. The author discovers that the resulting mathematical equivalences will enable us to use traditional linear forecasting methods within the context of the model but doing so destroys these same equivalences.

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