Nonlinear Signal Processing

Nonlinear Signal Processing: A Statistical Approach focuses on unifying the study of a broad and important class of nonlinear signal processing algorithms which emerge from statistical estimation principles, and where the underlying signals are non-Gaussian, rather than Gaussian, processes. Notably, by concentrating on just two non-Gaussian models, a large set of tools is developed that encompass a large portion of the nonlinear signal processing tools proposed in the literature over the past several decades. Key features include: * Numerous problems at the end of each chapter to aid development and understanding * Examples and case studies provided throughout the book in a wide range of applications bring the text to life and place the theory into context * A set of 60+ MATLAB software m-files allowing the reader to quickly design and apply any of the nonlinear signal processing algorithms described in the book to an application of interest is available on the accompanying FTP site.

Nonlinear signal and image processing methods are fast emerging as an alternative to established linear methods for meeting the challenges of increasingly sophisticated applications. Advances in computing performance and nonlinear theory are making nonlinear techniques not only viable, but practical. This book details recent advances in nonl

Signal processing, nonlinear data analysis, nonlinear time series, nonstationary processes.

Nonlinear Optical Systems: Principles, Phenomena, and Advanced Signal Processing is a simplified overview of the evolution of technology associated with nonlinear systems and advanced signal processing. This book’s coverage ranges from fundamentals to phenomena to the most cutting-edge aspects of systems for next-generation biomedical monitoring and nonlinear optical transmission. The authors address how these systems are applied through photonic signal processing in contemporary optical systems for communications and/or laser systems. They include a concise but sufficient explanation of mathematical representation of nonlinear equations to provide insight into nonlinear dynamics at different phases. The book also describes advanced aspects of solitons and bound solitons for passive- and active-mode locked fiber lasers, in which higher-order differential equations can be employed to represent the dynamics of amplitude evolution in the current or voltages of lightwaves in such systems. Covering a wide range of topics, this book: Introduces nonlinear systems and some mathematical representations, particularly the routes to chaos and bifurcation Describes nonlinear fiber lightwave lasing systems Covers nonlinear phenomena in fiber lasers, including both passive and active energy storage cavities Experimentally and theoretically demonstrates soliton pulses, in which lightwaves are the carrier under their envelopes Assembles and demonstrates sequences of both single and multiple solitons in a group and then assesses their dynamics in detail Examines the evolution of bound solitons, which are transmitted through single-mode optical fibers that compose a phase variation system This text outlines the theory and techniques used in nonlinear physics and applications for physical systems. It also illustrates the use of MATLAB® and Simulink® computer models and processing techniques for nonlinear signals. Building on readers’ newly acquired fundamental understanding of nonlinear systems and associated signal processing, the book then demonstrates the use of such applications in real-world, practical environments.

The function of a filter is to transform a signal into another one more suit able for a given purpose. As such, filters find applications in telecommunica tions, radar, sonar, remote sensing, geophysical signal processing, image pro cessing, and computer vision. Numerous authors have considered deterministic and statistical approaches for the study of passive, active, digital, multidimen sional, and adaptive filters. Most of the filters considered were linear although the theory of nonlinear filters is developing rapidly, as it is evident by the numerous research papers and a few specialized monographs now available. Our research interests in this area created opportunity for cooperation and co authored publications during the past few years in many nonlinear filter families described in this book. As a result of this cooperation and a visit from John Pitas on a research leave at the University of Toronto in September 1988, the idea for this book was first conceived. The difficulty in writing such a mono graph was that the area seemed fragmented and no general theory was available to encompass the many different kinds of filters presented in the literature. However, the similarities of some families of nonlinear filters and the need for such a monograph providing a broad overview of the whole area made the pro ject worthwhile. The result is the book now in your hands, typeset at the Department of Electrical Engineering of the University of Toronto during the summer of 1989.

This book provides an updated description of the most relevant types of highly nonlinear fibers. It also describes some of their actual applications for nonlinear optical signal processing. Multiple types of highly nonlinear fibers are considered, such as silica-based conventional highly nonlinear fibers, tapered fibers, photonic crystal fibers, and fibers made of highly nonlinear materials, namely lead-silicate, tellurite, bismuth oxide, and chalcogenide glasses. Several nonlinear phenomena occurring on such highly nonlinear fibers are described and used to realize different functions in the area of all-optical signal processing.  Describes several nonlinear phenomena occurring on optical fibers, namely nonlinear phase modulation, parametric and stimulated scattering processes, optical solitons, and supercontinuum generation.  Discusses different types of highly nonlinear fibers, namely silica-based conventional highly nonlinear fibers, tapered fibers, and photonic crystal fibers.  Examines fibers made of highly nonlinear materials, namely lead-silicate, tellurite, bismuth oxide, and chalcogenide glasses.  Describes the application of several nonlinear phenomena occurring on highly nonlinear fibers to realize different functions in the area of all-optical signal processing, namely optical amplification, multiwavelength sources, pulse generation, optical regeneration, wavelength conversion, and optical switching. Mário F. S. Ferreira received his PhD degree in 1992 in physics from the University of Aveiro, Portugal, where he is now a professor in the Physics Department. Between 1990 and 1991, he was at the University of Essex, UK, performing experimental work on external cavity semiconductor lasers and nonlinear optical fiber amplifiers. His research interests have been concerned with the modeling and characterization of multisection semiconductor lasers, quantum well lasers, optical fiber amplifiers and lasers, soliton propagation, nanophotonics, optical sensors, polarization, and nonlinear effects in optical fibers. He has written more than 400 scientific journal and conference publications and several books in the area of mathematical physics, optics, and photonics. He has served as chair and committee member of multiple international conferences, as well as guest editor and advisory board member of several international journals.

This straightforward text makes the complicated but powerful methods of non-linear control accessible to process engineers. Not only does it cover the necessary mathematics, but it consistently refers to the widely-known finite-dimensional linear time-invariant continuous case as a basis for extension to the nonlinear situation.