Wavelets: A concise guide
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Baltimore
Johns Hopkins Univ. Press
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XXIX, 270 S. graph. Darst. |
| ISBN: | 9781421404967 1421404966 9781421404950 1421404958 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
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| 003 | DE-604 | ||
| 005 | 20120821 | ||
| 007 | t | ||
| 008 | 120411s2012 d||| |||| 00||| eng d | ||
| 020 | |a 9781421404967 |9 978-1-4214-0496-7 | ||
| 020 | |a 1421404966 |9 1-4214-0496-6 | ||
| 020 | |a 9781421404950 |9 978-1-4214-0495-0 | ||
| 020 | |a 1421404958 |9 1-4214-0495-8 | ||
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| 035 | |a (DE-599)BVBBV040037448 | ||
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| 100 | 1 | |a Najmi, Amir-Homayoon |e Verfasser |0 (DE-588)1025085280 |4 aut | |
| 245 | 1 | 0 | |a Wavelets |b A concise guide |c Amir-Homayoon Najmi |
| 264 | 1 | |a Baltimore |b Johns Hopkins Univ. Press |c 2012 | |
| 300 | |a XXIX, 270 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Wavelet |0 (DE-588)4215427-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wavelet |0 (DE-588)4215427-3 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-024894189 | ||
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 450 N162 |
| DE-BY-FWS_katkey | 559509 |
| DE-BY-FWS_media_number | 083000514904 |
| _version_ | 1806623885699842048 |
| adam_text | Contents
List of Tables
xi
List of Figures
xiii
List of Acronyms
xix
Preface
xxi
Acknowledgments
xxix
1
Analysis in Vector and Function Spaces
1
1.1
Introduction
1
1.2
The Lebesgue Integral
3
1.3
Discrete Time Signals
5
1.4
Vector Spaces
5
1.5
Linear Independence
б
1.6
Bases and Basis Vectors
7
1.7
Normed Vector Spaces
8
1.8
Inner Product
9
1.9
Banach and Hubert Spaces
12
1.10
Linear Operators. Operator Norm, the Adjoint Operator
13
1.11
Reproducing Kernel Hubert Space
15
1.12
The Dirac Delta Distribution
18
1.13
Orthonormal
Vectors
20
1.14
Orthogonal Projections
21
1.15
Multi-Resolution Analysis Subspaces
22
1.16
Complete and
Orthonormal
Bases in L2
(Щ
25
1.17
The Dirac Notation
28
1.18
The Fourier Transform
31
1.19
The Fourier Series Expansion
34
1.20
The Discrete Time Fourier Transform
36
1.21
The Discrete Fourier Transform
37
1.22
Band-Limited Functions and the Sampling Theorem
38
vn
··· Contents
1.23 The Basis Operator in L2(K) 41
1.24 Biorthogonal Bases
and Representations
in L2 (K) 43
1.25 Frames in
a Finite Dimensional Vector Space
45
1.26
Frames in L2
(Ш)
50
1.27
Dual Frame Construction Algorithm
54
1.28
Exercises 56
2
Linear Time-Invariant Systems
59
2.1
Introduction 59
2.2
Convolution in Continuous Time
59
2.3
Convolution in Discrete Time
60
2.4
Convolution of Finite Length Sequences
61
2.5
Linear Time-Invariant Systems and the
Z
Transform
63
2.6
Spectral Factorization for Finite Length Sequences
66
2.7
Perfect Reconstruction Quadrature Mirror Filters
68
2.8
Exercises
73
3
Time, Frequency, and Scale Localizing Transforms
75
3.1
Introduction
75
3.2
The Windowed Fourier Transform
79
3.3
The Windowed Fourier Transform Inverse °1
3.4
The Range Space of the Windowed Fourier Transform
81
3.5
The Discretized Windowed Fourier Transform
83
3.6
Time-Frequency Resolution of the Windowed Fourier Transform
88
3.7
The Continuous Wavelet Transform
90
3.8
The Continuous Wavelet Transform Inverse
93
3.9
The Range Space of the Continuous Wavelet Transform
95
3.10
The Morlet, the Mexican Hat, and the
Haar
Wavelets
96
3.11
Discretizing the Continuous Wavelet Transform
101
3.12
Algorithm
A Trous
104
3.13
The Morlet Scalogram
107
3.14
Exercises
110
The
Haar
and Shannon Wavelets
4.1
Introduction 111
4.2 Haar
Multi-Resolution Analysis Subspaces
112
4.3
Summary and Generalization of Results
119
4.4
The Spectra of the
Haar
Filter Coefficients I22
4.5
Half-Band Finite Impulse Response Filters
4.6
The Shannon Scaling Function
Contents
їх
4.7
The Spectrum of the Shannon Filter Coefficients
130
4.8
Meyer s Wavelet
131
4.9
Exercises
133
5
General Properties of Scaling and Wavelet Functions
135
5.1
Introduction
135
5.2
Multi-Resolution Analysis Spaces
135
5.3
The Inverse Relations
140
5.4
The Shift-Invariant Discrete Wavelet Transform
143
5.5
Time Domain Properties
145
5.6
Examples of Finite Length Filter Coefficients
149
5.7
Frequency Domain Relations
150
5.8
Orthogonalization of a Basis Set: b Spline Wavelet
157
5.9
The Cascade Algorithm
159
5.10 Biorthogonal
Wavelets
163
5.11
Multi-
Resolution Analysis Using
Biorthogonal
Wavelets
167
5.12
Exercises
170
6
Discrete Wavelet Transform of Discrete Time Signals
173
6.1
Introduction
173
6.2
Discrete Time Data and Scaling Function Expansions
174
6.3
Implementing the DWTT for Even Length ho Filters
179
6.4
Denoising and Thresholding
185
6.5 Biorthogonal
Wavelets of Compact Support
187
6.6
The Lazy Filters
191
6.7
Exercises
191
7
Wavelet Regularity and Daubechies Solutions
193
7.1
Introduction
193
7.2
Zero Moments of the Mother Wavelet
194
7.3
The Form of H0(z) and the Decay Rate of
Φ(ω)
199
7.4
Daubechies Orthogonal Wavelets of Compact Support
200
7.5
Wavelet and Scaling Function Vanishing Moments
204
7.6 Biorthogonal
Wavelets of Compact Support
207
7.7 Biorthogonal
Spline Wavelets
211
7.8
The Lifting Scheme
215
7.9
Exercises
217
Contents
8 Orthogonal
Wavelet Packets
221
8.1
Introduction
221
8.2
Review of the Orthogonal Wavelet Transform
221
8.3
Packet Functions for
Orthonormal
Wavelets
224
8.4
Discrete Orthogonal Packet Transform of Finite Length Se¬
quences
231
8.5
The Best Basis Algorithm
236
8.6
Exercises
239
9
Wavelet Transform in Two Dimensions
241
9.1
Introduction
241
9.2
The Forward Transform
242
9.3
The Inverse Transform
247
9.4
Implementing the Two-Dimensional Wavelet Transform
248
9.5
Application to Image Compression
249
9.6
Image Fusion
257
9.7
Wavelet Descendants
258
9.8
Exercises
259
Bibliography
261
Index
267
MATHEMATICS
INTRODUCED NEARLY THREE DECADES AGO as a variable resolution
alternative to the Fourier transform, a wavelet is a short oscillatory wave¬
form for analysis of transients. The discrete wavelet transform has remarkable
multi-resolution and energy-compaction properties. Amir-Homayoon Najmi s
introduction to wavelet theory explains this mathematical concept clearly and
succinctly.
Wavelets are used in processing digital signals and imagery from myriad
sources. They form the backbone of the JPEG2000 compression standard, and
the Federal Bureau of Investigation uses
biorthogonal
wavelets to compress
and store its vast database of fingerprints.
Najmi
provides the mathemat¬
ics that demonstrate how wavelets work, describes how to construct them,
and discusses their importance as a tool to investigate and process signals
and imagery. He reviews key concepts such as frames, localizing transforms,
orthogonal and
biorthogonal
bases, and multi-resolution. His examples in¬
clude the
Haar,
the Shannon, and the Daubechies families of orthogonal and
biorthogonal
wavelets.
Our capacity and need for collecting and transmitting digital data is
increasing at an astonishing rate. So too is the importance of wavelets to
anyone working with and analyzing digital data. Najmi s primer will be an
indispensable resource for those in computer science, the physical sciences,
applied mathematics, and engineering who wish to obtain an in-depth under¬
standing and working knowledge of this fascinating and evolving field.
Amir-Homayoon
Najmi
completed the Mathematical Tripos at Cambridge
University and obtained his D.Phil, at Oxford University. He is with the Johns
Hopkins University s Applied Physics Laboratory and is a faculty member of
the Whiting School of Engineering
CE
programs in applied physics and elec¬
trical engineering.
THE JOHNS HOPKINS UNIVERSITY PRESS
BALTIMORE I WWW.PRESS.JHU.EDU
Cover design: Martha Sewall
Cover illustration: Continuous wavelet transform
coefficients of a bowhead whale sound.
©
A. H.
Najmi
ISBN-
13: 978-1-4214-0496-7
ISBN-10:
1-4214-0496-6
9»781421ll404967
|
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| indexdate | 2024-08-06T09:53:18Z |
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| language | English |
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| spellingShingle | Najmi, Amir-Homayoon Wavelets A concise guide Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | Wavelets A concise guide |
| title_auth | Wavelets A concise guide |
| title_exact_search | Wavelets A concise guide |
| title_full | Wavelets A concise guide Amir-Homayoon Najmi |
| title_fullStr | Wavelets A concise guide Amir-Homayoon Najmi |
| title_full_unstemmed | Wavelets A concise guide Amir-Homayoon Najmi |
| title_short | Wavelets |
| title_sort | wavelets a concise guide |
| title_sub | A concise guide |
| topic | Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Wavelet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894189&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894189&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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Inhaltsverzeichnis
THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 450 N162 |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |