Nonlinear signal processing using empirical global dynamical equations

A method for determining a set of differential dynamical equations of motion which approximate an underlying generating process is outlined. The method can recover a system of equations with good predictive ability using just a few data points. The method differs markedly from current techniques, which calculate iterative mapping functions or perform phase space smoothing using only geometric information. Results of the application of this method to real-world systems, including extraction of a human voice from broadband mechanical noise at level down to -30-dB signal to noise ratio, using no prior knowledge of the signal or noise characteristics are presented