A First Course on Wavelets
Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. 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. 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:
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.
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Review: A First Course on WaveletsUser Review - Zhitao Fan - Goodreads
An introductory level wavelet book. The author organize it in his own understanding and it basically includes all the elementary mathematical analysis of wavelet. Ch 1,2,3,4,7 gives the details of ... Read full review
Bases for L²R
12 Orthonormal bases generated by a single function the BalianLow theorem
13 Smooth projections on L²R
14 Local sine and cosine bases and the construction of some wavelets
15 The unitary folding operators and the smooth projections
16 Notes and references
Multiresolution analysis and the construction of wavelets
61 Wavelets and sampling theorems
62 LittlewoodPaley theory
63 Necessary tools
64 The Lebesgue spaces LpR with 1 p oo
65 The Hardy space HlR
66 The Sobolev spaces LPSR 1 p oo s 123
67 The Lipschitz spaces AQ R 0 a 1 and the Zygmund class A R
21 Multiresolution analysis
22 Construction of wavelets from a multiresolution analysis
23 The construction of compactly supported wavelets
24 Better estimates for the smoothness of compactly supported wavelets
25 Notes and references
33 The LemariéMeyer wavelets revisited
34 Characterization of some bandlimited wavelets
35 Notes and references
Other constructions of wavelets
42 Spline wavelets on the real line
43 Orthonormal bases of piecewise linear continuous functions for L2T
44 Orthonormal bases of periodic splines
45 Periodization of wavelets defined on the real line
Representation of functions by wavelets
52 Unconditional bases for Banach spaces
53 Convergence of wavelet expansions in V
54 Pointwise convergence of wavelet expansions
55 H¹ and BMO on R
56 Wavelets as unconditional bases for HR and V with 1 p oo
57 Notes and references
Characterizations of function spaces using wavelets
Characterizations in the theory of wavelets
71 The basic equations
72 Some applications of the basic equations
73 The characterization of MRA wavelets
74 A characterization of lowpass filters
75 A characterization of scaling functions
76 Nonexistence of smooth wavelets in H²R
81 The reconstruction formula for frames
82 The BalianLow theorem for frames
83 Frames from translations and dilations
84 Smooth frames forH²l
Discrete transforms and algorithms
92 The discrete cosine transform DCT and the fast cosine transform FCT
93 The discrete version of the local sine and cosine bases
94 Decomposition and reconstruction algorithms for wavelets
95 Wavelet packets
96 Notes and references
A Primer on Wavelets and Their Scientific Applications
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Limited preview - 1999
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Limited preview - 2000
JSTOR: A First Course on Wavelets
Just the right thing for a first course on wavelets. The subsequent chapters, nine in all, contain the essential information about or- thonormal wavelets. ...
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#1 Book: A first course on wavelets A First Course on Wavelets Eugenio Hernandez and Guido Weiss A Volume in the Studies in Advanced Mathematics Series ...
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A first course on wavelets / Eugenio Hernández, Guido Weiss. Author:. Hernández, Eugenio, 1954-. Subjects:. Wavelets (Mathematics). Publisher: ...
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A First Course on Wavelets (Studies in Advanced Mathematics)(页1 ...
[attach]2084[/attach]Title: A First Course on waveletsauthor: Eugenio hernandezpublisher: CRC-presspublication Date: 1996-09-12Number Of Pages: 489Wavelet ...
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A FIRST COURSE ON WAVELETS: en su libreria Casa del Libro
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A first course on wavelets. » Наука » Теория обработки сигналов. Начало « Наука « Математика « Теория обработки сигналов «...
A FIRST COURSE ON WAVELETS. -. HERNANDEZ, EUGENIO, WEISS, GUIDO. 489 p -24 cm x cm. 0849382742. QA403.3 H43 1996 E.2. No Posee ...
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Journal of Approximation Theory : Measures, densities and ...
E. Hernandez and G. Weiss, A First Course on Wavelets, CRC Press, Boca Raton, FL (1996). rl Long, Multidimensional Wavelet Analysis, ...
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A First Course on WAVELETS Author : E. Hernandez and G. Weiss, CRC press, 1996 Wavelets in the Signal Processing A Wavelet Tour of Signal Processing ...
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