Wavelets and Signal Processing


Book Description

Provides a digest of the current developments, open questions and unsolved problems likely to determine a new frontier for future advanced study and research in the rapidly growing areas of wavelets, wavelet transforms, signal analysis, and signal and image processing. Ideal reference work for advanced students and practitioners in wavelets, and wavelet transforms, signal processing and time-frequency signal analysis. Professionals working in electrical and computer engineering, applied mathematics, computer science, biomedical engineering, physics, optics, and fluid mechanics will also find the book a valuable resource.




Time-Frequency Signal Analysis and Processing


Book Description

Time-Frequency Signal Analysis and Processing (TFSAP) is a collection of theory, techniques and algorithms used for the analysis and processing of non-stationary signals, as found in a wide range of applications including telecommunications, radar, and biomedical engineering. This book gives the university researcher and R&D engineer insights into how to use TFSAP methods to develop and implement the engineering application systems they require. New to this edition: - New sections on Efficient and Fast Algorithms; a "Getting Started" chapter enabling readers to start using the algorithms on simulated and real examples with the TFSAP toolbox, compare the results with the ones presented in the book and then insert the algorithms in their own applications and adapt them as needed. - Two new chapters and twenty three new sections, including updated references. - New topics including: efficient algorithms for optimal TFDs (with source code), the enhanced spectrogram, time-frequency modelling, more mathematical foundations, the relationships between QTFDs and Wavelet Transforms, new advanced applications such as cognitive radio, watermarking, noise reduction in the time-frequency domain, algorithms for Time-Frequency Image Processing, and Time-Frequency applications in neuroscience (new chapter). - A comprehensive tutorial introduction to Time-Frequency Signal Analysis and Processing (TFSAP), accessible to anyone who has taken a first course in signals - Key advances in theory, methodology and algorithms, are concisely presented by some of the leading authorities on the respective topics - Applications written by leading researchers showing how to use TFSAP methods




Wavelet Transforms and Their Applications


Book Description

Overview Historically, the concept of "ondelettes" or "wavelets" originated from the study of time-frequency signal analysis, wave propagation, and sampling theory. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean MorIet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. However, this new concept can be viewed as the synthesis of various ideas originating from different disciplines including mathematics (Calder6n-Zygmund operators and Littlewood-Paley theory), physics (coherent states in quantum mechanics and the renormalization group), and engineering (quadratic mirror filters, sideband coding in signal processing, and pyramidal algorithms in image processing). Wavelet analysis is an exciting new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines, and improvement in CAT scans and other medical image technology. Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms, called the fundamental building blocks, at different positions and scales and subsequently reconstructed with high precision.




Wavelet Transforms and Time-Frequency Signal Analysis


Book Description

The last fifteen years have produced major advances in the mathematical theory of wavelet transforms and their applications to science and engineering. In an effort to inform researchers in mathematics, physics, statistics, computer science, and engineering and to stimulate furtherresearch, an NSF-CBMS Research Conference on Wavelet Analysis was organized at the University of Central Florida in May 1998. Many distinguished mathematicians and scientists from allover the world participated in the conference and provided a digest of recent developments, open questions, and unsolved problems in this rapidly growing and important field. As a follow-up project, this monograph was developed from manuscripts sub mitted by renowned mathematicians and scientists who have made important contributions to the subject of wavelets, wavelet transforms, and time-frequency signal analysis. This publication brings together current developments in the theory and applications of wavelet transforms and in the field of time-frequency signal analysis that are likely to determine fruitful directions for future advanced study and research.




Foundations of Time-Frequency Analysis


Book Description

Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.




Signal Analysis


Book Description

Signal analysis gives an insight into the properties of signals and stochastic processes by methodology. Linear transforms are integral to the continuing growth of signal processes as they characterize and classify signals. In particular, those transforms that provide time-frequency signal analysis are attracting greater numbers of researchers and are becoming an area of considerable importance. The key characteristic of these transforms, along with a certain time-frequency localization called the wavelet transform and various types of multirate filter banks, is their high computational efficiency. It is this computational efficiently which accounts for their increased application. This book provides a complete overview and introduction to signal analysis. It presents classical and modern signal analysis methods in a sequential structure starting with the background to signal theory. Progressing through the book the author introduces more advanced topics in an easy to understand style. Including recent and emerging topics such as filter banks with perfect reconstruction, time frequency and wavelets. With great accuracy and technical merit, this book makes a useful and original contribution to the current literature.




Practical Time-Frequency Analysis


Book Description

Time frequency analysis has been the object of intense research activity in the last decade. This book gives a self-contained account of methods recently introduced to analyze mathematical functions and signals simultaneously in terms of time and frequency variables. The book gives a detailed presentation of the applications of these transforms to signal processing, emphasizing the continuous transforms and their applications to signal analysis problems, including estimation, denoising, detection, and synthesis. To help the reader perform these analyses, Practical Time-Frequency Analysis provides a set of useful tools in the form of a library of S functions, downloadable from the authors' Web sites in the United States and France. - Detailed presentation of the Wavelet and Gabor transforms - Applications to deterministic and random signal theory - Spectral analysis of nonstationary signals and processes - Numerous practical examples ranging from speech analysis to underwater acoustics, earthquake engineering, internet traffic, radar signal denoising, medical data interpretation, etc - Accompanying software and data sets, freely downloadable from the book's Web page




Wavelets


Book Description

The last two subjects mentioned in the title "Wavelets, Time Frequency Methods and Phase Space" are so well established that they do not need any explanations. The first is related to them, but a short introduction is appropriate since the concept of wavelets emerged fairly recently. Roughly speaking, a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position pa rameter. Many of the ideas and techniques related to such expansions have existed for a long time and are widely used in mathematical analysis, theoretical physics and engineering. However, the rate of progress increased significantly when it was realized that these ideas could give rise to straightforward calculational methods applicable to different fields. The interdisciplinary structure (R.C.P. "Ondelettes") of the C.N.R.S. and help from the Societe Nationale Elf-Aquitaine greatly fostered these developments. The conference, the proceedings of which are contained in this volume, was held at the Centre National de Rencontres Mathematiques (C.N.R.M) in Marseille from December 14-18, 1987 and bought together an interdisciplinary mix of par ticipants. We hope that these proceedings will convey to the reader some of the excitement and flavor of the meeting.




Condition Monitoring with Vibration Signals


Book Description

Provides an extensive, up-to-date treatment of techniques used for machine condition monitoring Clear and concise throughout, this accessible book is the first to be wholly devoted to the field of condition monitoring for rotating machines using vibration signals. It covers various feature extraction, feature selection, and classification methods as well as their applications to machine vibration datasets. It also presents new methods including machine learning and compressive sampling, which help to improve safety, reliability, and performance. Condition Monitoring with Vibration Signals: Compressive Sampling and Learning Algorithms for Rotating Machines starts by introducing readers to Vibration Analysis Techniques and Machine Condition Monitoring (MCM). It then offers readers sections covering: Rotating Machine Condition Monitoring using Learning Algorithms; Classification Algorithms; and New Fault Diagnosis Frameworks designed for MCM. Readers will learn signal processing in the time-frequency domain, methods for linear subspace learning, and the basic principles of the learning method Artificial Neural Network (ANN). They will also discover recent trends of deep learning in the field of machine condition monitoring, new feature learning frameworks based on compressive sampling, subspace learning techniques for machine condition monitoring, and much more. Covers the fundamental as well as the state-of-the-art approaches to machine condition monitoringguiding readers from the basics of rotating machines to the generation of knowledge using vibration signals Provides new methods, including machine learning and compressive sampling, which offer significant improvements in accuracy with reduced computational costs Features learning algorithms that can be used for fault diagnosis and prognosis Includes previously and recently developed dimensionality reduction techniques and classification algorithms Condition Monitoring with Vibration Signals: Compressive Sampling and Learning Algorithms for Rotating Machines is an excellent book for research students, postgraduate students, industrial practitioners, and researchers.




Signal Analysis


Book Description

Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more