Wavelet Transforms and Their Applications

Description

This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals Front Matter....Pages i-xv Brief Historical Introduction....Pages 1-27 Hilbert Spaces and Orthonormal Systems....Pages 29-127 Fourier Transforms and Their Applications....Pages 129-242 The Gabor Transform and Time–Frequency Signal Analysis....Pages 243-286 The Wigner–Ville Distribution and Time–Frequency Signal Analysis....Pages 287-336 The Wavelet Transforms and Their Basic Properties....Pages 337-373 Multiresolution Analysis and Construction of Wavelets....Pages 375-440 Extensions of Multiresolution Analysis....Pages 441-473 Newland’s Harmonic Wavelets....Pages 475-487 Wavelet Transform Analysis of Turbulence....Pages 489-516 Back Matter....Pages 517-553