Wavelet Based Analysis and Software for Multi-Scale Fractal Processes

摘要

This final technical reporte summarizes the technical objectives, work accomplished, results, and technical feasibility. The primary objective of this research is to develop methodology and software for the analysis of atmospheric turbulence and related data. Turbulence data are challenging because they are inherently non-stationary across a range of scales. Because the discrete wavelet transform is a natural tool for use with non-stationary and scale-dependent data, we investigate the efficacy of a variety of wavelet-based techniques including approximate maximum likelihood and least squares estimators of power-law processes. These estimators are adapted to work effectively in the presence of (i) slow variations in the power-law parameters, (ii) large-scale stochastic trends and (iii) small-scale non-turbulent events. We examine the statistical properties of (most) wavelet-based power-law parameter estimators and develop corresponding confidence intervals. We also assess the efficacy of nonlinear deterministic models for turbulence data. All software was implemented in MathSoft's next generation S+WAVELETS module.