Discovering Wavelets

The last 15 years have seen an explosion of interest in wavelets with applications in fields such as image compression, turbulence, human vision, radar and earthquake prediction. Wavelets represent an area that combines signal in image processing, mathematics, physics and electrical engineering. As such, this title is intended for the wide audience that is interested in mastering the basic techniques in this subject area, such as decomposition and compression.

A comprehensive, step-by-step introduction to wavelets in statistics. What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for «time-scale» applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly «discovered» mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, Vidakovic compiles, organizes, and explains in depth research data previously available only in disparate journal articles. He carefully balances both statistical and mathematical techniques, supplementing the material with a wealth of examples, more than 100 illustrations, and extensive references-with data sets and S-Plus wavelet overviews made available for downloading over the Internet. Both introductory and data-oriented modeling topics are featured, including: * Continuous and discrete wavelet transformations. * Statistical optimality properties of wavelet shrinkage. * Theoretical aspects of wavelet density estimation. * Bayesian modeling in the wavelet domain. * Properties of wavelet-based random functions and densities. * Several novel and important wavelet applications in statistics. * Wavelet methods in time series. Accessible to anyone with a background in advanced calculus and algebra, Statistical Modeling by Wavelets promises to become the standard reference for statisticians and engineers seeking a comprehensive introduction to an emerging field.

Delivers an appropriate mix of theory and applications to help readers understand the process and problems of image and signal analysis Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and revised coverage throughout with an emphasis on key and recent developments in the field of signal and image processing. Topical coverage includes: vector spaces, signals, and images; the discrete Fourier transform; the discrete cosine transform; convolution and filtering; windowing and localization; spectrograms; frames; filter banks; lifting schemes; and wavelets. Discrete Fourier Analysis and Wavelets introduces a new chapter on frames—a new technology in which signals, images, and other data are redundantly measured. This redundancy allows for more sophisticated signal analysis. The new coverage also expands upon the discussion on spectrograms using a frames approach. In addition, the book includes a new chapter on lifting schemes for wavelets and provides a variation on the original low-pass/high-pass filter bank approach to the design and implementation of wavelets. These new chapters also include appropriate exercises and MATLAB® projects for further experimentation and practice. • Features updated and revised content throughout, continues to emphasize discreteand digital methods, and utilizes MATLAB® to illustrate these concepts • Contains two new chapters on frames and lifting schemes, which take into account crucial new advances in the field of signal and image processing • Expands the discussion on spectrograms using a frames approach, which is an ideal method for reconstructing signals after information has been lost or corrupted (packet erasure) • Maintains a comprehensive treatment of linear signal processing for audio and image signals with a well-balanced and accessible selection of topics that appeal to a diverse audience within mathematics and engineering • Focuses on the underlying mathematics, especially the concepts of finite-dimensional vector spaces and matrix methods, and provides a rigorous model for signals and images based on vector spaces and linear algebra methods • Supplemented with a companion website containing solution sets and software exploration support for MATLAB and SciPy (Scientific Python) Thoroughly class-tested over the past fifteen years, Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing is an appropriately self-contained book ideal for a one-semester course on the subject. S. Allen Broughton, PhD, is Professor Emeritus of Mathematics at Rose-Hulman Institute of Technology. Dr. Broughton is a member of the American Mathematical Society (AMS) and the Society for the Industrial Applications of Mathematics (SIAM), and his research interests include the mathematics of image and signal processing, and wavelets. Kurt Bryan, PhD, is Professor of Mathematics at Rose-Hulman Institute of Technology. Dr. Bryanis a member of MAA and SIAM and has authored over twenty peer-reviewed journal articles. Kurt Bryan, PhD, is Professor of Mathematics at Rose-Hulman Institute of Technology. Dr. Bryanis a member of MAA and SIAM and has authored over twenty peer-reviewed journal articles.Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and r

Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling ? self-similarity, long-range dependence and multi-fractals ? are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.

The first book on the subject. Written by an acknowledged expert in the field. The techniques discussed have important applications to wireless engineering. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Discovering the Solar System, Second Edition covers the Sun, the planets, their satellites and the host of smaller bodies that orbit the Sun. This book offers a comprehensive introduction to the subject for science students, and examines the discovery, investigation and modelling of these bodies. Following a thematic approach, chapters cover interiors, surfaces and the atmospheres of major bodies, including the Earth. The book starts with an overview of the Solar System and its origin, and then takes a look at small bodies, such as asteroids, comets and meteorites. Carefully balancing breadth of coverage with depth, Discovering the Solar System, Second Edition: Offers a comprehensive introduction, assuming little prior knowledge Includes full coverage of each planet, as well as the moon, Europa and Titan. The Second Edition includes new material on exoplanetary systems, and a general update throughout. Presents latest results from the Mars Rover and Cassini-Huygens missions Includes a colour plate section Contains ‘stop and think’ questions embedded in the text to aid understanding, along with questions at the end of major sections. Answers are provided at the end of the book. Provides summaries at the end of each chapter, and a glossary at the end of the book Praise for the First Edition: «(…) essential reading for all undergraduate students (…) and for those at a more advanced level approaching the subject for the first time.» THE SCIENCE BOOK BOARD BOOK REVIEW “One of the best books on the solar system I have seen. The general accuracy and quality of the content is excellent.” JOURNAL OF THE BRITISH ASTRONOMICAL ASSOCIATION

Superconductivity is a quantum phenomenon that manifests itself in materials showing zero electrical resistance below a characteristic temperature resulting in the potential for an electric current to run continually through such a material without the need for a power source. Such materials are used extensively in medical and power applications, e.g. MRI and NMR machines. Discovering Superconductivity uses a series of practical and investigative activities, which can be used as tutor demonstrations or as student lab exercises. This highly illustrated text features the following sections: Introduction – including a brief history of superconductivity Superconductivity – an explanation of the phenomenon and its effects Superconducting materials – including High & Low temperature superconductors Applications – how superconductivity is used in medical imaging, at CERN and in the Maglev trains This text will serve as an excellent introduction for students, with or without a physics background, to superconductivity. With a strong practical, experimental emphasis, it provides readers with an overview of the topic preparing them for more advanced texts used in advanced undergraduate and post-graduate courses. PowerPoint files of the figures presented within this text are available at: booksupport.wiley.com A word from the author: «The intention of this text is to introduce the reader to the study of superconductivity via a minds-on approach .... The minds-on approach takes this a stage further by requiring the learner to engage with the process to a greater extent.»

The European Young Chemist Award has now been awarded four times (2006, 2008, 2010 and 2012). The authors of the previous books based on the competition have become some of the leading scientists in Europe. These books truly provide a glimpse into the future research landscape of European chemistry. Fifteen top contributions have been selected for this single volume covering areas of chemistry and materials science. The broad range of themes is presented in an approachable and readable manner equally appropriate for non-specialists on the topic. The overview of intriguing topics includes chemical synthesis and advanced methodologies as well as materials, nanoscience and nanotechnologies.

Surveying Cultures uniquely employs techniques rooted in survey methodology to discover cultural patterns in social science research. Examining both classical and emerging methods that are used to survey and assess differing norms among populations, the book successfully breaks new ground in the field, introducing a theory of measurement for ethnographic studies that employs the consensus-as-culture model. The book begins with a basic overview of cross-cultural measurement of sentiments and presents innovative and sophisticated analyses of measurement issues and of homogeneity among respondents. Subsequent chapters explore topics that are at the core of successful data collection and analysis in culture studies, including: The role of bipolar scales and Internet data collection in measuring sentiments Key methodological variables that determine the quality of quantitative data, including measurement errors, validity, and reliability New approaches to reliability and several new methods of assessing a respondent's degree of inculcation into group culture Sampling, coverage, nonresponse, and measurement errors, with an in-depth discussion of their occurrence in culture surveys, their impact assessments, and how current measurement techniques are constructed to help prevent these kinds of errors Common problems often encountered in the acquisition and communication of data, including identifying error variances, interpreting gender differences in responses, and defining the difference between cultures and subcultures Throughout the book, each topic is accompanied by a review of related methodological literature. For many of the presented concepts, the author includes a formal analysis of the related issues in measuring cultural norms and reports on analyses. Each chapter concludes with an organized list of major findings as well as an insightful outline of specific recommendations regarding practical problems in culture studies. Surveying Cultures serves as a valuable supplemental book to courses on survey and research methods at the upper-undergraduate and graduate levels. It is also an excellent reference for researchers in the fields of sociology, anthropology, psychology, and political science.

The field of data mining lies at the confluence of predictive analytics, statistical analysis, and business intelligence. Due to the ever-increasing complexity and size of data sets and the wide range of applications in computer science, business, and health care, the process of discovering knowledge in data is more relevant than ever before. This book provides the tools needed to thrive in today’s big data world. The author demonstrates how to leverage a company’s existing databases to increase profits and market share, and carefully explains the most current data science methods and techniques. The reader will “learn data mining by doing data mining”. By adding chapters on data modelling preparation, imputation of missing data, and multivariate statistical analysis, Discovering Knowledge in Data, Second Edition remains the eminent reference on data mining. The second edition of a highly praised, successful reference on data mining, with thorough coverage of big data applications, predictive analytics, and statistical analysis. Includes new chapters on Multivariate Statistics, Preparing to Model the Data, and Imputation of Missing Data, and an Appendix on Data Summarization and Visualization Offers extensive coverage of the R statistical programming language Contains 280 end-of-chapter exercises Includes a companion website for university instructors who adopt the book