New Methods for Nonlinear Tracking and Nonlinear Chaotic Signal Processing

Abstract

Abstract : The aim of the current research is to establish that we can identify/classify the individual signals that make up the total signal. The algorithm can function either as a detection algorithm or as an algorithm for preliminary processing leading to actual separation and cleaning of signals. It is not currently possible to do this latter task, even in the simplest situation, without first determining what signals are to be separated. We imagine that we have a library of samples of signals from sources of interest. An incoming signal is received that is a sum of one or more of the signals in the library plus noise, and we wish to determine which signals are actually present (i.e., we want to identify the source of the signal) and what are the relative amplitudes of the signals. We assume that some, perhaps all, of the signals have a broad frequency spectrum so that conventional linear filtering is inadequate. It is further assumed that we have samples of the individual signals in a library, although if they are broad-band chaotic, the signals will not be identical. One or more of the signals may be noise with its own characteristics. To illustrate that we can actually accomplish this, we will present the results of some simulations. In the figures on the following pages are some samples of the signals we have been working with. Figures 1 and 2 present time traces and Figures 3 and 4 are the corresponding spectra. The signals labelled 3 and 7 are random gaussian noise with a spectrum chosen to coincide with that of one of the other signals. Two of the signals, 4 and 5, are from electronic circuits and the rest are the solutions of some nonlinear differential equations. From the spectra we can see that there is little