Firdous A. Shah – författare

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.

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.

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 endThe 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 book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors’ teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India.