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Fundamentals of Wavelets: Theory, Algorithms, and Applications 2nd edition [Kõva köide]

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(University of Birmingham UK),
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Fundamentals of Wavelets: Theory, Algorithms, and Applications 2nd editionSuurem pilt
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Püsilink: https://www.kriso.ee/db/9780470484135.html
Märksõnad:
"Most existing books on wavelets are either too mathematical or they focus on too narrow a specialty. This book provides a thorough treatment of the subject from an engineering point of view. It is a one-stop source of theory, algorithms, applications, and computer codes related to wavelets. This second edition has been updated by the addition of: a section on "Other Wavelets" that describes curvelets, ridgelets, lifting wavelets, etc a section on lifting algorithms"--

"Most existing books on wavelets are either too mathematical or they focus on too narrow a specialty. This book provides a thorough treatment of the subject from an engineering point of view. It is a one-stop source of theory, algorithms, applications, and computer codes related to wavelets. This second edition has been updated by the addition of: a section on "Other Wavelets" that describes curvelets, ridgelets, lifting wavelets, etc. a section on lifting algorithms Sections on Edge Detection and Geophysical Applications Section on Multiresolution Time Domain Method (MRTD) and on Inverse problems."--

Provided by publisher.

Most existing books on wavelets are either too mathematical or they focus on too narrow a specialty. This book provides a thorough treatment of the subject from an engineering point of view. It is a one-stop source of theory, algorithms, applications, and computer codes related to wavelets. This second edition has been updated by the addition of:
  • a section on "Other Wavelets" that describes curvelets, ridgelets, lifting wavelets, etc
  • a section on lifting algorithms
  • Sections on Edge Detection and Geophysical Applications
  • Section on Multiresolution Time Domain Method (MRTD) and on Inverse problems

Arvustused

"This book provides a thorough treatment of wavelet theory and is very convenient for graduate students and researchers in electrical engineering, physics, and applied mathematics." (Zentralblatt MATH, 2011)  

Preface to the Second Edition xv
Preface to the First Edition xvii
1 What Is This Book All About?
1(5)
2 Mathematical Preliminary
6(28)
2.1 Linear Spaces
6(2)
2.2 Vectors and Vector Spaces
8(3)
2.3 Basis Functions, Orthogonality, and Biorthogonality
11(3)
2.3.1 Example
11(1)
2.3.2 Orthogonality and Biorthogonality
11(3)
2.4 Local Basis and Riesz Basis
14(3)
2.4.1 Haar Basis
15(1)
2.4.2 Shannon Basis
15(2)
2.5 Discrete Linear Normed Space
17(1)
2.5.1 Example 1
17(1)
2.5.2 Example 2
18(1)
2.6 Approximation by Orthogonal Projection
18(1)
2.7 Matrix Algebra and Linear Transformation
19(6)
2.7.1 Elements of Matrix Algebra
20(1)
2.7.2 Eigenmatrix
21(1)
2.7.3 Linear Transformation
22(1)
2.7.4 Change of Basis
23(1)
2.7.5 Hermitian Matrix, Unitary Matrix, and Orthogonal Transformation
24(1)
2.8 Digital Signals
25(6)
2.8.1 Sampling of Signal
25(1)
2.8.2 Linear Shift-Invariant Systems
26(1)
2.8.3 Convolution
26(2)
2.8.4 z-Transform
28(1)
2.8.5 Region of Convergence
29(2)
2.8.6 Inverse z-transform
31(1)
2.9 Exercises
31(2)
2.10 References
33(1)
3 Fourier Analysis
34(27)
3.1 Fourier Series
34(2)
3.2 Examples
36(3)
3.2.1 Rectified Sine Wave
36(1)
3.2.2 Comb Function and the Fourier Series Kernel KN(t)
37(2)
3.3 Fourier Transform
39(2)
3.4 Properties of Fourier Transform
41(3)
3.4.1 Linearity
41(1)
3.4.2 Time Shifting and Time Scaling
41(1)
3.4.3 Frequency Shifting and Frequency Scaling
42(1)
3.4.4 Moments
42(1)
3.4.5 Convolution
43(1)
3.4.6 Parseval's Theorem
43(1)
3.5 Examples of Fourier Transform
44(3)
3.5.1 The Rectangular Pulse
44(1)
3.5.2 The Triangular Pulse
45(1)
3.5.3 The Gaussian Function
46(1)
3.6 Poisson's Sum and Partition of Unity
47(4)
3.6.1 Partition of Unity
49(2)
3.7 Sampling Theorem
51(2)
3.8 Partial Sum and Gibb's Phenomenon
53(1)
3.9 Fourier Analysis of Discrete-Time Signals
54(4)
3.9.1 Discrete Fourier Basis and Discrete Fourier Series
54(2)
3.9.2 Discrete-Time Fourier Transform (DTFT)
56(2)
3.10 Discrete Fourier Transform (DFT)
58(1)
3.11 Exercises
59(1)
3.12 References
60(1)
4 Time-Frequency Analysis
61(33)
4.1 Window Function
63(1)
4.2 Short-Time Fourier Transform
64(4)
4.2.1 Inversion Formula
65(1)
4.2.2 Gabor Transform
66(1)
4.2.3 Time-Frequency Window
66(1)
4.2.4 Properties of STFT
67(1)
4.3 Discrete Short-Time Fourier Transform
68(2)
4.4 Discrete Gabor Representation
70(1)
4.5 Continuous Wavelet Transform
71(5)
4.5.1 Inverse Wavelet Transform
73(1)
4.5.2 Time-Frequency Window
74(2)
4.6 Discrete Wavelet Transform
76(1)
4.7 Wavelet Series
77(1)
4.8 Interpretations of the Time-Frequency Plot
78(2)
4.9 Wigner-Ville Distribution
80(3)
4.9.1 Gaussian Modulated Chirp
81(1)
4.9.2 Sinusoidal Modulated Chirp
82(1)
4.9.3 Sinusoidal Signal
83(1)
4.10 Properties of Wigner-Ville Distribution
83(3)
4.10.1 A Real Quantity
85(1)
4.10.2 Marginal Properties
85(1)
4.10.3 Correlation Function
86(1)
4.11 Quadratic Superposition Principle
86(2)
4.12 Ambiguity Function
88(1)
4.13 Exercises
89(1)
4.14 Computer Programs
90(3)
4.14.1 Short-Time Fourier Transform
90(1)
4.14.2 Wigner-Ville Distribution
91(2)
4.15 References
93(1)
5 Multiresolution Analysis
94(20)
5.1 Multiresolution Spaces
95(2)
5.2 Orthogonal, Biorthogonal, and Semiorthogonal Decomposition
97(4)
5.3 Two-Scale Relations
101(1)
5.4 Decomposition Relation
102(1)
5.5 Spline Functions and Properties
103(5)
5.5.1 Properties of Splines
107(1)
5.6 Mapping a Function into MRA Space
108(2)
5.6.1 Linear Splines (m = 2)
109(1)
5.6.2 Cubic Splines (m = 4)
109(1)
5.7 Exercises
110(2)
5.8 Computer Programs
112(1)
5.8.1 B-splines
112(1)
5.9 References
113(1)
6 Construction of Wavelets
114(33)
6.1 Necessary Ingredients for Wavelet Construction
115(4)
6.1.1 Relationship between the Two-Scale Sequences
115(2)
6.1.2 Relationship between Reconstruction and Decomposition Sequences
117(2)
6.2 Construction of Semiorthogonal Spline Wavelets
119(4)
6.2.1 Expression for {go[ k]}
119(2)
6.2.2 Remarks
121(2)
6.3 Construction of Orthonormal Wavelets
123(1)
6.4 Orthonormal Scaling Functions
124(12)
6.4.1 Shannon Scaling Function
124(2)
6.4.2 Meyer Scaling Function
126(3)
6.4.3 Battle-Lemarie Scaling Function
129(1)
6.4.4 Daubechies Scaling Function
130(6)
6.5 Construction of Biorthogonal Wavelets
136(2)
6.6 Graphical Display of Wavelet
138(3)
6.6.1 Iteration Method
138(1)
6.6.2 Spectral Method
139(1)
6.6.3 Eigenvalue Method
140(1)
6.7 Exercises
141(3)
6.8 Computer Programs
144(2)
6.8.1 Daubechies Wavelet
144(1)
6.8.2 Iteration Method
145(1)
6.9 References
146(1)
7 DWT and Filter Bank Algorithms
147(50)
7.1 Decimation and Interpolation
147(8)
7.1.1 Decimation
148(3)
7.1.2 Interpolation
151(3)
7.1.3 Convolution Followed by Decimation
154(1)
7.1.4 Interpolation Followed by Convolution
154(1)
7.2 Signal Representation in the Approximation Subspace
155(2)
7.3 Wavelet Decomposition Algorithm
157(2)
7.4 Reconstruction Algorithm
159(2)
7.5 Change of Bases
161(3)
7.6 Signal Reconstruction in Semiorthogonal Subspaces
164(6)
7.6.1 Change of Basis for Spline Functions
164(4)
7.6.2 Change of Basis for Spline Wavelets
168(2)
7.7 Examples
170(2)
7.8 Two-Channel Perfect Reconstruction Filter Bank
172(17)
7.8.1 Spectral-Domain Analysis of a Two-Channel PR Filter Bank
176(8)
7.8.2 Time-Domain Analysis
184(5)
7.9 Polyphase Representation for Filter Banks
189(2)
7.9.1 Signal Representation in Polyphase Domain
189(1)
7.9.2 Filter Bank in the Polyphase Domain
189(2)
7.10 Comments on DWT and PR Filter Banks
191(1)
7.11 Exercises
192(1)
7.12 Computer Programs
193(2)
7.12.1 Decomposition and Reconstruction Algorithm
193(2)
7.13 References
195(2)
8 Special Topics in Wavelets and Algorithms
197(42)
8.1 Fast Integral Wavelet Transform
198(22)
8.1.1 Finer Time Resolution
198(3)
8.1.2 Finer Scale Resolution
201(3)
8.1.3 Function Mapping into the Interoctave Approximation Subspaces
204(3)
8.1.4 Examples
207(13)
8.2 Ridgelet Transform
220(2)
8.3 Curvelet Transform
222(2)
8.4 Complex Wavelets
224(5)
8.4.1 Linear Phase Biorthogonal Approach
227(1)
8.4.2 Quarter-Shift Approach
228(1)
8.4.3 Common Factor Approach
228(1)
8.5 Lifting Wavelet Transform
229(8)
8.5.1 Linear Spline Wavelet
233(1)
8.5.2 Construction of Scaling Function and Wavelet from Lifting Scheme
234(1)
8.5.3 Linear Interpolative Subdivision
234(3)
8.6 References
237(2)
9 Digital Signal Processing Applications
239(69)
9.1 Wavelet Packet
240(3)
9.2 Wavelet-Packet Algorithms
243(3)
9.3 Thresholding
246(2)
9.3.1 Hard Thresholding
246(1)
9.3.2 Soft Thresholding
246(1)
9.3.3 Percentage Thresholding
247(1)
9.3.4 Implementation
247(1)
9.4 Interference Suppression
248(4)
9.4.1 Best Basis Selection
249(3)
9.5 Faulty Bearing Signature Identification
252(4)
9.5.1 Pattern Recognition of Acoustic Signals
252(2)
9.5.2 Wavelets, Wavelet Packets, and FFT Features
254(2)
9.6 Two-Dimensional Wavelets and Wavelet Packets
256(8)
9.6.1 Two-Dimensional Wavelets
256(2)
9.6.2 Two-Dimensional Wavelet Packets
258(1)
9.6.3 Two-Dimensional Wavelet Algorithm
259(3)
9.6.4 Wavelet Packet Algorithm
262(2)
9.7 Edge Detection
264(3)
9.7.1 Sobel Edge Detector
265(1)
9.7.2 Laplacian of Gaussian Edge Detector
265(1)
9.7.3 Canny Edge Detector
266(1)
9.7.4 Wavelet Edge Detector
266(1)
9.8 Image Compression
267(10)
9.8.1 Basics of Data Compression
267(4)
9.8.2 Wavelet Tree Coder
271(1)
9.8.3 EZW Code
272(1)
9.8.4 EZW Example
272(3)
9.8.5 Spatial Oriented Tree (SOT)
275(2)
9.8.6 Generalized Self-Similarity Tree (GST)
277(1)
9.9 Microcalcification Cluster Detection
277(7)
9.9.1 CAD Algorithm Structure
278(1)
9.9.2 Partitioning of Image and Nonlinear Contrast Enhancement
278(1)
9.9.3 Wavelet Decomposition of the Subimages
278(1)
9.9.4 Wavelet Coefficient Domain Processing
279(2)
9.9.5 Histogram Thresholding and Dark Pixel Removal
281(1)
9.9.6 Parametric ART2 Clustering
282(1)
9.9.7 Results
282(2)
9.10 Multicarrier Communication Systems (MCCS)
284(3)
9.10.1 OFDM Multicarrier Communication Systems
284(1)
9.10.2 Wavelet Packet-Based MCCS
285(2)
9.11 Three-Dimensional Medical Image Visualization
287(6)
9.11.1 Three-Dimensional Wavelets and Algorithms
288(2)
9.11.2 Rendering Techniques
290(1)
9.11.3 Region of Interest
291(1)
9.11.4 Summary
291(2)
9.12 Geophysical Applications
293(6)
9.12.1 Boundary Value Problems and Inversion
294(1)
9.12.2 Well Log Analysis
295(1)
9.12.3 Reservoir Data Analysis
296(2)
9.12.4 Downhole Pressure Gauge Data Analysis
298(1)
9.13 Computer Programs
299(6)
9.13.1 Two-Dimensional Wavelet Algorithms
299(4)
9.13.2 Wavelet Packet Algorithms
303(2)
9.14 References
305(3)
10 Wavelets in Boundary Value Problems
308(45)
10.1 Integral Equations
309(4)
10.2 Method of Moments
313(1)
10.3 Wavelet Techniques
314(8)
10.3.1 Use of Fast Wavelet Algorithm
314(1)
10.3.2 Direct Application of Wavelets
315(2)
10.3.3 Wavelets in Spectral Domain
317(5)
10.3.4 Wavelet Packets
322(1)
10.4 Wavelets on the Bounded Interval
322(2)
10.5 Sparsity and Error Considerations
324(3)
10.6 Numerical Examples
327(7)
10.7 Semiorthogonal versus Orthogonal Wavelets
334(1)
10.8 Differential Equations
335(11)
10.8.1 Multigrid Method
336(1)
10.8.2 Multiresolution Time Domain (MRTD) Method
337(1)
10.8.3 Haar-MRTD Derivation
338(3)
10.8.4 Subcell Modeling in MRTD
341(2)
10.8.5 Examples
343(3)
10.9 Expressions for Splines and Wavelets
346(2)
10.10 References
348(5)
Index 353
Jaideva C. Goswami, PhD, is an Engineering Advisor at Schlumberger in Sugarland, Texas. He is also a former professor of Electronics and Communication Engineering at the Indian Institute of Technology, Kharagpur. Dr. Goswami has taught several short courses on wavelets and contributed to the Wiley Encyclopedia of Electrical and Electronics Engineering as well as Wiley Encyclopedia of RF and Microwave Engineering. He has many research papers and patents to his credit, and is a Fellow of IEEE.

Andrew K. Chan, PhD, is on the faculty of Texas A&M University and is the coauthor of Wavelets in a Box and Wavelet Toolware. He is a Life Fellow of IEEE.