This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets. The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows.
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These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis MRA is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets. Some of the topics treated include: Several bases generated by a single function via translations and dilations Multiresolution analysis, compactly supported wavelets, and spline wavelets Band-limited wavelets Unconditionality of wavelet bases Characterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions The authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations, and that most properties and constructions of wavelets can be developed using these two equations.
Material related to applications is provided, and constructions of splines wavelets are presented. Mathematicians, engineers, physicists, and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets. Product details Format Hardback pages Dimensions x x Other books in this series.
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The fundamental construction of these functions by means of "multiresolution analyses" is presented; in particular, this method is used for introducing the spline wavelets and the compactly supported wavelets. An important feature of this book, however, is the use of the Fourier transform for studying wavelets on the real line.
A simple characterization of all wavelets is presented which is most useful for the construction of new families of wavelets. This technique can also be used for obtaining characterizations of low pass filters and scaling functions. Another feature is the use of wavelets for representing those function spaces that are most often encountered in analysis: the Lebesgue spaces, Hardy spaces, and more generally, the Besov spaces, the Sobolev, and the Lipschitz spaces. Other topics, some related to applications, are also included: the Fast Fourier Transform, wavelet packets, frames, local cosine and sine bases and their discrete versions are just some examples.
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A First Course in Wavelets with Fourier Analysis
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis.
Subsequent chapters feature:. Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform. Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets.
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New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis , Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
a first course in wavelets with fourier analysis solution manual pdf
Albert Boggess , Francis J. A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis , Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video.
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