CHAOS AND FRACTAL ALGORITHMS APPLIED TO SIGNAL-PROCESSING AND ANALYSIS

Modern signal processing methods strive to maximize signal to noise ratios, even in the presence of severe noise. Frequently, real world data is degraded by under sampling of intrinsic periodicities, or by sampling with unevenly spaced intervals. This results in dropout or missing data, and such data sets are particularly difficult to process using conventional methods. In many cases, one must still extract as much information as possible from a given data set, although the available discrete data is sparse or very noisy. In such cases, we have found the algorithms derived from Chaos and fractal theory to represent a viable alternative to traditional spectral analysis. The data analysis techniques discussed in this work include phase space reconstruction, Poincare projections radius of gyration exponent, artificial insymmetration patterns (AIP), Liapunov spectra, correlation techniques, R/S analysis, K-factor, fractal statistics, maximum entropy method, and wavelets.