Time Frequency and Time-Scale Methodes

The goal of the book is to develop a deeper understanding of the roles of time-frequency or Fourier and Gabor analysis, and time-scale or wavelet analysis, when the various tools are properly assembled in a larger context. While researchers at the forefront of developments in time-frequency scale (TFS) analysis are well aware of the benefits of such a unified approach, there remains a gap in the larger community of practitioners concerning precisely the strengths and limitations of Gabor analysis versus wavelets. The book fills this gap by presenting the interface between time-frequency and time-scale methods as a rich area of work. Topics and features: • Addresses new TFS methods and algorithms • Presents an integrated approach to using Fourier/Gabor methods and wavelet methods • Real world applications of Gabor theory, wavelets to PDEs and wavelets to compression • Develops the ideas of phase space and the uncertainty principle focusing on the role of the metaplectic group and the flexibility in constructing analysis tools • Explanations at the end of each chapter address historical context, major developments and new directions. Fast track route to mastering all aspects of time management Covers all the key techniques for managing your time successfully, from clearing your desk to prioritisation, and from good delegation to knowing how and when to say 'no' Examples and lessons from some of the world's most successful time managers, and ideas from the smartest thinkers, including Robert Paterson, Don Aslett and Stephen Covey Includes a glossary of key concepts and a comprehensive resources guide ExpressExec is a unique business resource of one hundred books. These books present the best current thinking and span the entire range of contemporary business practice. Each book gives you the key concepts behind the subject and the techniques to implement the ideas effectively, together with lessons from benchmark companies and ideas from the world's smartest thinkers. ExpressExec is organised into ten core subject areas making it easy to find the information you need: 01 Innovation 02 Enterprise 03 Strategy 04 Marketing 05 Finance 06 Operations and Technology 07 Organizations 08 Leading 09 People 10 Life and Work ExpressExec is a perfect learning solution for people who need to master the latest business thinking and practice quickly. Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of developments in time-frequency and time-scale analysis are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. Cover......Page 1 Time-Frequency and Time-Scale Methods......Page 2 Contents......Page 5 Preface......Page 11 1 Wavelets: Basic properties, parameterizations and sampling......Page 19 2 Derivatives and multiwavelets......Page 59 3 Sampling in Fourier and wavelet analysis......Page 107 4 Bases for time-frequency analysis......Page 181 5 Fourier uncertainty principles......Page 209 6 Function spaces and operator theory......Page 263 7 Uncertainty principles in mathematical physics......Page 303 A Appendix......Page 377 References......Page 387 Index......Page 405 "Applied mathematicians and engineers in signal/image processing and communication theory will find in the first half of the book an accessible presentation of principal developments in this active field of modern analysis, as well as the mathematical methods underlying real-world applications. Researchers and students in mathematical analysis, signal analysis, and mathematical physics will benefit from the coverage of deep mathematical advances featured in the second part of the work."--BOOK JACKET Presents a fast track route to mastering various aspects of time management. This title covers key techniques for managing your time successfully, from clearing your desk to prioritisation, and from good delegation to knowing how and when to say 'no'. Wavelets play a fundamental role in decomposing the function spacesand operators that act on themthat are considered throughout this book.