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AuthorNievergelt, Yves. author
TitleWavelets Made Easy [electronic resource] / by Yves Nievergelt
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1999
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Descript XI, 297 p. 1 illus. online resource


This book, written at the level of a first course in calculus and linear algebra, offers a lucid and concise explanation of mathematical wavelets. Evolving from ten years of classroom use, its accessible presentation is designed for undergraduates in a variety of disciplines (computer science, engineering, mathematics, mathematical sciences) as well as for practising professionals in these areas. This unique text starts the first chapter with a description of the key features and applications of wavelets, focusing on Haar's wavelets but using only high school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra. The second part of this book provides the foundations of least squares approximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particular attention is paid to Daubechies wavelets. Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the classroom as well as a valuable resource for self-study


A Algorithms for Wavelet Transforms -- 1 Haarโ{128}{153}s Simple Wavelets -- 2 Multidimensional Wavelets and Applications -- 3 Algorithms for Daubechies Wavelets -- B Basic Fourier Analysis -- 4 Inner Products and Orthogonal Projections -- 5 Discrete and Fast Fourier Transforms -- 6 Fourier Series for Periodic Functions -- C Computation and Design of Wavelets -- 7 Fourier Transforms on the Line and in Space -- 8 Daubechies Wavelets Design -- 9 Signal Representations with Wavelets -- D Directories -- Acknowledgments -- Collection of Symbols

Mathematics Functional analysis Applied mathematics Engineering mathematics Electrical engineering Mathematics Applications of Mathematics Functional Analysis Electrical Engineering


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