Wavelet techniques for chaotic and fractal dynamics

Abstract

A novel wavelet based denoising technique is developed and shown to be more effective on average than waveshrink in denoising contaminated chaotic signals. A chaotic beam experiment is used to verify its effectiveness.Correlation dimension (D2) convergence issues for stochastic colored noise processes are revisited with the Gaussian Spectral Synthesis method. The inadequacies of the Phase Randomization method are discussed and is shown to be an inappropriate means to investigate D 2 convergence.A ensemble of nonlinear and linear measures is used to assess determinism and existing fractal structure in RR intervals from over 50 heart patients. Techniques are critiqued for their ability to classify disease states of the heart and predict the onset of fatal cardiac rhythms.