Time Frequency and Time-Scale Methodes

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 these areas 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. "Foundations of Time-Frequency and Time-Scale Methods" will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics. 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. "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 book-cover.pdf......Page 1 frontmatter.pdf......Page 2 chapter1.pdf......Page 19 chapter2.pdf......Page 59 chapter3.pdf......Page 107 chapter4.pdf......Page 181 chapter5.pdf......Page 209 chapter6.pdf......Page 263 chapter7.pdf......Page 303 apps-ref-ind.pdf......Page 377 Wavelets play a fundamental role in decomposing the function spacesand operators that act on themthat are considered throughout this book.