Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.

The only integrative approach to chaos and random fractal theory Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and apply novel methods to effectively solve their signal processing problems. Multiscale Analysis of Complex Time Series fills this pressing need by presenting chaos and random fractal theory in a unified manner. Adopting a data-driven approach, the book covers: DNA sequence analysis EEG analysis Heart rate variability analysis Neural information processing Network traffic modeling Economic time series analysis And more Additionally, the book illustrates almost every concept presented through applications and a dedicated Web site is available with source codes written in various languages, including Java, Fortran, C, and MATLAB, together with some simulated and experimental data. The only modern treatment of signal processing with chaos and random fractals unified, this is an essential book for researchers and graduate students in electrical engineering, computer science, bioengineering, and many other fields.

The thesis provides a detailed analysis of the independence structure possessed by multiscale models and demonstrates that such an analysis provides important insight into the multiscale stochastic realization problem. Multiscale models constitute a broad class of probabilistic models which includes the well--known subclass of multiscale autoregressive (MAR) models. MAR models have proven useful in a variety of different application areas, due to the fact that they provide a rich set of tools for various signal processing tasks. In order to use these tools, however, a MAR or multiscale model must first be constructed to provide an accurate probabilistic description of the particular application at hand. This thesis addresses this issue of multiscale model identification or realization. Previous work in the area of MAR model identification has focused on developing algorithms which decorrelate certain subsets of random vectors in an effort to design an accurate model. In this thesis, we develop a set-theoretic and graph-theoretic framework for better understanding these types of realization algorithms and for the purpose of designing new such algorithms.

The application of modern methods in numerical mathematics on problems in chemical engineering is essential for designing, analyzing and running chemical processes and even entire plants. Scientific Computing in Chemical Engineering II gives the state of the art from the point of view of numerical mathematicians as well as that of engineers. The present volume as part of a two-volume edition covers topics such as computer-aided process design, combustion and flame, image processing, optimization, control, and neural networks. The volume is aimed at scientists, practitioners and graduate students in chemical engineering, industrial engineering and numerical mathematics.