The neighborhood method and its coupling with the wavelet method for signal separation of chaotic signals

Signal separation, i.e., the elimination or suppression of extraneous components from measured signals, is an essential module of modern signal analysis. We report the development of two novel signal separation methods - (i) the neighborhood method (NM) and (ii) a modified wavelet method (MWM) - that seem to be aptly suited for signals acquired from machining process sensors, i.e., for chaotic signals with small, uniform Lyapunov exponents. For the NM, a variant of shadowing signal separation methods used for signal separation of chaotic signals, we establish theoretical bounds on performance under various noisy conditions and analyze its algorithmic complexity. Our MWM is an adaptation of Donoho's wavelet method to nonlinear, and possibly chaotic, signals with multiplicative noise. It incorporates certain features of the NM and it has lower algorithmic complexity than the NM, and is, therefore, more suitable for on-line implementation. Both methods were tested on chaotic signals corresponding to the reconstructed Rossler attractor. A discussion on the application of both methods to signals obtained from actual machining process sensors is provided in order to motivate their suitability to real-world nonlinear processes.