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.
Wavelet Transforms: Kith and Kin serves as an introduction to contemporary aspects of time-frequency analysis encompassing the theories of Fourier transforms, wavelet transforms and their respective offshoots. This book is the first of its kind totally devoted to the treatment of continuous signals and it systematically encompasses the theory of Fourier transforms, wavelet transforms, geometrical wavelet transforms and their ramifications. The authors intend to motivate and stimulate interest among mathematicians, computer scientists, engineers and physical, chemical and biological scientists. The text is written from the ground up with target readers being senior undergraduate and first-year graduate students and it can serve as a reference for professionals in mathematics, engineering and applied sciences. Features Flexibility in the book’s organization enables instructors to select chapters appropriate to courses of different lengths, emphasis and levels of difficulty Self-contained, the text provides an impetus to the contemporary developments in the signal processing aspects of wavelet theory at the forefront of research A large number of worked-out examples are included Every major concept is presented with explanations, limitations and subsequent developments, with emphasis on applications in science and engineering A wide range of exercises are incoporated in varying levels from elementary to challenging so readers may develop both manipulative skills in theory wavelets and deeper insight Answers and hints for selected exercises appear at the end The origin of the theory of wavelet transforms dates back to the 1980s as an outcome of the intriguing efforts of mathematicians, physicists and engineers. Owing to the lucid mathematical framework and versatile applicability, the theory of wavelet transforms is now a nucleus of shared aspirations and ideas.
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.
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