Wavelet Theory

A self-contained, elementary introduction to wavelet theory andapplications
Exploring the growing relevance of wavelets in the field ofmathematics, Wavelet Theory: An Elementary Approach withApplications provides an introduction to the topic, detailing thefundamental concepts and presenting its major impacts in the worldbeyond academia. Drawing on concepts from calculus and linearalgebra, this book helps readers sharpen their mathematical proofwriting and reading skills through interesting, real-worldapplications.
The book begins with a brief introduction to the fundamentals ofcomplex numbers and the space of square-integrable functions. Next,Fourier series and the Fourier transform are presented as tools forunderstanding wavelet analysis and the study of wavelets in thetransform domain. Subsequent chapters provide a comprehensivetreatment of various types of wavelets and their related concepts,such as Haar spaces, multiresolution analysis, Daubechies wavelets,and biorthogonal wavelets. In addition, the authors include twochapters that carefully detail the transition from wavelet theoryto the discrete wavelet transformations. To illustrate therelevance of wavelet theory in the digital age, the book includestwo in-depth sections on current applications: the FBI WaveletScalar Quantization Standard and image segmentation.
In order to facilitate mastery of the content, the book featuresmore than 400 exercises that range from theoretical tocomputational in nature and are structured in a multi-part formatin order to assist readers with the correct proof or solution.These problems provide an opportunity for readers to furtherinvestigate various applications of wavelets. All problems arecompatible with software packages and computer labs that areavailable on the book's related Web site, allowing readers toperform various imaging/audio tasks, explore computer wavelettransformations and their inverses, and visualize the applicationsdiscussed throughout the book.
Requiring only a prerequisite knowledge of linear algebra andcalculus, Wavelet Theory is an excellent book for courses inmathematics, engineering, and physics at the upper-undergraduatelevel. It is also a valuable resource for mathematicians,engineers, and scientists who wish to learn about wavelet theory onan elementary level.