This book illustrates how modern mathematical wavelet transform techniques offer fresh insights into the complex behavior of neural systems at different levels: from the microscopic dynamics of individual cells to the macroscopic behavior of large neural networks. It also demonstrates how and where wavelet-based mathematical tools can provide an advantage over classical approaches used in neuroscience. The authors well describe single neuron and populational neural recordings. This 2nd edition discusses novel areas and significant advances resulting from experimental techniques and computational approaches developed since 2015, and includes three new topics: • Detection of fEPSPs in multielectrode LFPs recordings. • Analysis of Visual Sensory Processing in the Brain and BCI for Human Attention Control; • Analysis and Real-time Classification of Motor-related EEG Patterns; The book is a valuable resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in these and related areas.
This book examines theoretical and applied aspects of wavelet analysis in neurophysics, describing in detail different practical applications of the wavelet theory in the areas of neurodynamics and neurophysiology and providing a review of fundamental work that has been carried out in these fields over the last decade. Chapters 1 and 2 introduce and review the relevant foundations of neurophysics and wavelet theory, respectively, pointing on one hand to the various current challenges in neuroscience and introducing on the other the mathematical techniques of the wavelet transform in its two variants (discrete and continuous) as a powerful and versatile tool for investigating the relevant neuronal dynamics. Chapter 3 then analyzes results from examining individual neuron dynamics and intracellular processes. The principles for recognizing neuronal spikes from extracellular recordings and the advantages of using wavelets to address these issues are described and combined with approaches based on wavelet neural networks (chapter 4). The features of time-frequency organization of EEG signals are then extensively discussed, from theory to practical applications (chapters 5 and 6). Lastly, the technical details of automatic diagnostics and processing of EEG signals using wavelets are examined (chapter 7). The book will be a useful resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduat e students specializing in the corresponding areas.
Signal Processing for Neuroscientists introduces analysis techniques primarily aimed at neuroscientists and biomedical engineering students with a reasonable but modest background in mathematics, physics, and computer programming. The focus of this text is on what can be considered the 'golden trio' in the signal processing field: averaging, Fourier analysis, and filtering. Techniques such as convolution, correlation, coherence, and wavelet analysis are considered in the context of time and frequency domain analysis. The whole spectrum of signal analysis is covered, ranging from data acquisition to data processing; and from the mathematical background of the analysis to the practical application of processing algorithms. Overall, the approach to the mathematics is informal with a focus on basic understanding of the methods and their interrelationships rather than detailed proofs or derivations. One of the principle goals is to provide the reader with the background required to understand the principles of commercially available analyses software, and to allow him/her to construct his/her own analysis tools in an environment such as MATLAB®. - Multiple color illustrations are integrated in the text - Includes an introduction to biomedical signals, noise characteristics, and recording techniques - Basics and background for more advanced topics can be found in extensive notes and appendices - A Companion Website hosts the MATLAB scripts and several data files: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123708670
A comprehensive guide to the conceptual, mathematical, and implementational aspects of analyzing electrical brain signals, including data from MEG, EEG, and LFP recordings. This book offers a comprehensive guide to the theory and practice of analyzing electrical brain signals. It explains the conceptual, mathematical, and implementational (via Matlab programming) aspects of time-, time-frequency- and synchronization-based analyses of magnetoencephalography (MEG), electroencephalography (EEG), and local field potential (LFP) recordings from humans and nonhuman animals. It is the only book on the topic that covers both the theoretical background and the implementation in language that can be understood by readers without extensive formal training in mathematics, including cognitive scientists, neuroscientists, and psychologists. Readers who go through the book chapter by chapter and implement the examples in Matlab will develop an understanding of why and how analyses are performed, how to interpret results, what the methodological issues are, and how to perform single-subject-level and group-level analyses. Researchers who are familiar with using automated programs to perform advanced analyses will learn what happens when they click the “analyze now” button. The book provides sample data and downloadable Matlab code. Each of the 38 chapters covers one analysis topic, and these topics progress from simple to advanced. Most chapters conclude with exercises that further develop the material covered in the chapter. Many of the methods presented (including convolution, the Fourier transform, and Euler's formula) are fundamental and form the groundwork for other advanced data analysis methods. Readers who master the methods in the book will be well prepared to learn other approaches.
Electroencephalograms (EEGs) are becoming increasingly important measurements of brain activity and they have great potential for the diagnosis and treatment of mental and brain diseases and abnormalities. With appropriate interpretation methods they are emerging as a key methodology to satisfy the increasing global demand for more affordable and effective clinical and healthcare services. Developing and understanding advanced signal processing techniques for the analysis of EEG signals is crucial in the area of biomedical research. This book focuses on these techniques, providing expansive coverage of algorithms and tools from the field of digital signal processing. It discusses their applications to medical data, using graphs and topographic images to show simulation results that assess the efficacy of the methods. Additionally, expect to find: explanations of the significance of EEG signal analysis and processing (with examples) and a useful theoretical and mathematical background for the analysis and processing of EEG signals; an exploration of normal and abnormal EEGs, neurological symptoms and diagnostic information, and representations of the EEGs; reviews of theoretical approaches in EEG modelling, such as restoration, enhancement, segmentation, and the removal of different internal and external artefacts from the EEG and ERP (event-related potential) signals; coverage of major abnormalities such as seizure, and mental illnesses such as dementia, schizophrenia, and Alzheimer’s disease, together with their mathematical interpretations from the EEG and ERP signals and sleep phenomenon; descriptions of nonlinear and adaptive digital signal processing techniques for abnormality detection, source localization and brain-computer interfacing using multi-channel EEG data with emphasis on non-invasive techniques, together with future topics for research in the area of EEG signal processing. The information within EEG Signal Processing has the potential to enhance the clinically-related information within EEG signals, thereby aiding physicians and ultimately providing more cost effective, efficient diagnostic tools. It will be beneficial to psychiatrists, neurophysiologists, engineers, and students or researchers in neurosciences. Undergraduate and postgraduate biomedical engineering students and postgraduate epileptology students will also find it a helpful reference.
An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method. - The first book to present a unified view of filtering techniques - Concentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time series - Provides easy access to a wide spectrum of parametric and non-parametric filtering methods
Wavelets seem to be the most efficient tool in signal denoising and compression. They can be used in an unlimited number of applications in all fields of chemistry where the instrumental signals are the source of information about the studied chemical systems or phenomena, and in all cases where these signals have to be archived. The quality of the instrumental signals determines the quality of answer to the basic analytical questions: how many components are in the studied systems, what are these components like and what are their concentrations? Efficient compression of the signal sets can drastically speed up further processing such as data visualization, modelling (calibration and pattern recognition) and library search. Exploration of the possible applications of wavelets in analytical chemistry has just started and this book will significantly speed up the process. The first part, concentrating on theoretical aspects, is written in a tutorial-like manner, with simple numerical examples. For the reader's convenience, all basic terms are explained in detail and all unique properties of wavelets are pinpointed and compared with the other types of basis function. The second part presents applications of wavelets from many branches of chemistry which will stimulate chemists to further exploration of this exciting subject.
This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ÉcolePolytechnique in Paris. - Provides a broad perspective on the principles and applications of transient signal processing with wavelets - Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms - Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements - Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet - Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition - Optical flow calculation and video compression algorithms - Image models with bounded variation functions - Bayes and Minimax theories for signal estimation - 200 pages rewritten and most illustrations redrawn - More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics
The comprehensive compendium furnishes a quick and efficient entry point to many multiresolution techniques and facilitates the transition from an idea into a real project. It focuses on methods combining several soft computing techniques (fuzzy logic, neural networks, genetic algorithms) in a multiresolution framework.Illustrated with numerous vivid examples, this useful volume gives the reader the necessary theoretical background to decide which methods suit his/her needs.New materials and applications for multiresolution analysis are added, including notable research topics such as deep learning, graphs, and network analysis.
Although Digital Signal Processing (DSP) has long been considered an electrical engineering topic, recent developments have also generated significant interest from the computer science community. DSP applications in the consumer market, such as bioinformatics, the MP3 audio format, and MPEG-based cable/satellite television have fueled a desire to understand this technology outside of hardware circles. Designed for upper division engineering and computer science students as well as practicing engineers and scientists, Digital Signal Processing Using MATLAB & Wavelets, Second Edition emphasizes the practical applications of signal processing. Over 100 MATLAB examples and wavelet techniques provide the latest applications of DSP, including image processing, games, filters, transforms, networking, parallel processing, and sound. This Second Edition also provides the mathematical processes and techniques needed to ensure an understanding of DSP theory. Designed to be incremental in difficulty, the book will benefit readers who are unfamiliar with complex mathematical topics or those limited in programming experience. Beginning with an introduction to MATLAB programming, it moves through filters, sinusoids, sampling, the Fourier transform, the z-transform and other key topics. Two chapters are dedicated to the discussion of wavelets and their applications. A CD-ROM (platform independent) accompanies the book and contains source code, projects for each chapter, and the figures from the book.
