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Introduction to Orthogonal Transforms: With Applications in Data Processing and Analysis [Hardback]

(Harvey Mudd College, California)
  • Formāts: Hardback, 590 pages, height x width x depth: 252x179x30 mm, weight: 1290 g, Worked examples or Exercises; 5 Tables, black and white; 24 Halftones, black and white; 167 Line drawings, black and white
  • Izdošanas datums: 08-Mar-2012
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521516889
  • ISBN-13: 9780521516884
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Introduction to Orthogonal Transforms: With Applications in Data Processing and AnalysisPalielināt
  • Formāts: Hardback, 590 pages, height x width x depth: 252x179x30 mm, weight: 1290 g, Worked examples or Exercises; 5 Tables, black and white; 24 Halftones, black and white; 167 Line drawings, black and white
  • Izdošanas datums: 08-Mar-2012
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521516889
  • ISBN-13: 9780521516884
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780521516884.html
Keywords:
A systematic, unified treatment of orthogonal transform methods for signal processing, data analysis and communications, this book guides the reader from mathematical theory to problem solving in practice. It examines each transform method in depth, emphasizing the common mathematical principles and essential properties of each method in terms of signal decorrelation and energy compaction. The different forms of Fourier transform, as well as the Laplace, Z-, WalshHadamard, Slant, Haar, KarhunenLočve and wavelet transforms, are all covered, with discussion of how each transform method can be applied to real-world experimental problems. Numerous practical examples and end-of-chapter problems, supported by online Matlab and C code and an instructor-only solutions manual, make this an ideal resource for students and practitioners alike.

Papildus informācija

A systematic, unified treatment of orthogonal transform methods that guides the reader from mathematical theory to problem solving in practice.
Preface xii
Acknowledgments xx
Notation xxi
1 Signals and systems
1(33)
1.1 Continuous and discrete signals
1(3)
1.2 Unit step and nascent delta functions
4(3)
1.3 Relationship between complex exponentials and delta functions
7(2)
1.4 Attributes of signals
9(2)
1.5 Signal arithmetics and transformations
11(4)
1.6 Linear and time-invariant systems
15(2)
1.7 Signals through continuous LTI systems
17(4)
1.8 Signals through discrete LTI systems
21(3)
1.9 Continuous and discrete convolutions
24(5)
1.10 Homework problems
29(5)
2 Vector spaces and signal representation
34(71)
2.1 Inner product space
34(23)
2.1.1 Vector space
34(2)
2.1.2 Inner product space
36(7)
2.1.3 Bases of vector space
43(4)
2.1.4 Signal representation by orthogonal bases
47(5)
2.1.5 Signal representation by standard bases
52(3)
2.1.6 An example: the Fourier transforms
55(2)
2.2 Unitary transformation and signal representation
57(13)
2.2.1 Linear transformation
57(2)
2.2.2 Eigenvalue problems
59(2)
2.2.3 Eigenvectors of D2 as Fourier basis
61(3)
2.2.4 Unitary transformations
64(2)
2.2.5 Unitary transformations in N-D space
66(4)
2.3 Projection theorem and signal approximation
70(11)
2.3.1 Projection theorem and pseudo-inverse
70(6)
2.3.2 Signal approximation
76(5)
2.4 Frames and biorthogonal bases
81(12)
2.4.1 Frames
81(1)
2.4.2 Signal expansion by frames and Riesz bases
82(8)
2.4.3 Frames in finite-dimensional space
90(3)
2.5 Kernel function and Mercer's theorem
93(6)
2.6 Summary
99(2)
2.7 Homework problems
101(4)
3 Continuous-time Fourier transform
105(41)
3.1 The Fourier series expansion of periodic signals
105(14)
3.1.1 Formulation of the Fourier expansion
105(2)
3.1.2 Physical interpretation
107(2)
3.1.3 Properties of the Fourier series expansion
109(2)
3.1.4 The Fourier expansion of typical functions
111(8)
3.2 The Fourier transform of non-periodic signals
119(23)
3.2.1 Formulation of the CTFT
119(5)
3.2.2 Relation to the Fourier expansion
124(1)
3.2.3 Properties of the Fourier transform
125(7)
3.2.4 Fourier spectra of typical functions
132(8)
3.2.5 The uncertainty principle
140(2)
3.3 Homework problems
142(4)
4 Discrete-time Fourier transform
146(74)
4.1 Discrete-time Fourier transform
146(27)
4.1.1 Fourier transform of discrete signals
146(5)
4.1.2 Properties of the DTFT
151(6)
4.1.3 DTFT of typical functions
157(3)
4.1.4 The sampling theorem
160(10)
4.1.5 Reconstruction by interpolation
170(3)
4.2 Discrete Fourier transform
173(28)
4.2.1 Formulation of the DFT
173(6)
4.2.2 Array representation
179(4)
4.2.3 Properties of the DFT
183(9)
4.2.4 Four different forms of the Fourier transform
192(4)
4.2.5 DFT computation and fast Fourier transform
196(5)
4.3 Two-dimensional Fourier transform
201(14)
4.3.1 Two-dimensional signals and their spectra
201(3)
4.3.2 Fourier transform of typical 2-D functions
204(3)
4.3.3 Four forms of 2-D Fourier transform
207(2)
4.3.4 Computation of the 2-D DFT
209(6)
4.4 Homework problems
215(5)
5 Applications of the Fourier transforms
220(57)
5.1 LTI systems in time and frequency domains
220(5)
5.2 Solving differential and difference equations
225(7)
5.3 Magnitude and phase filtering
232(6)
5.4 Implementation of 1-D filtering
238(11)
5.5 Implementation of 2-D filtering
249(7)
5.6 Hilbert transform and analytic signals
256(5)
5.7 Radon transform and image restoration from projections
261(8)
5.8 Orthogonal frequency-division modulation (OFDM)
269(2)
5.9 Homework problems
271(6)
6 The Laplace and z-transforms
277(62)
6.1 The Laplace transform
277(34)
6.1.1 From Fourier transform to Laplace transform
277(3)
6.1.2 The region of convergence
280(1)
6.1.3 Properties of the Laplace transform
281(3)
6.1.4 The Laplace transform of typical signals
284(2)
6.1.5 Analysis of continuous LTI systems by Laplace transform
286(6)
6.1.6 First-order system
292(3)
6.1.7 Second-order system
295(12)
6.1.8 The unilateral Laplace transform
307(4)
6.2 The z-transform
311(24)
6.2.1 From Fourier transform to z-transform
311(3)
6.2.2 Region of convergence
314(2)
6.2.3 Properties of the z-transform
316(5)
6.2.4 The z-transform of typical signals
321(1)
6.2.5 Analysis of discrete LTI systems by z-transform
322(5)
6.2.6 First- and second-order systems
327(5)
6.2.7 The unilateral z-transform
332(3)
6.3 Homework problems
335(4)
7 Fourier-related orthogonal transforms
339(40)
7.1 The Hartley transform
339(14)
7.1.1 Continuous Hartley transform
339(2)
7.1.2 Properties of the Hartley transform
341(2)
7.1.3 Hartley transform of typical signals
343(2)
7.1.4 Discrete Hartley transform
345(3)
7.1.5 The 2-D Hartley transform
348(5)
7.2 The discrete sine and cosine transforms
353(24)
7.2.1 The continuous cosine and sine transforms
353(2)
7.2.2 From DFT to DCT and DST
355(5)
7.2.3 Matrix forms of DCT and DST
360(6)
7.2.4 Fast algorithms for the DCT and DST
366(4)
7.2.5 DOT and DST filtering
370(3)
7.2.6 The 2-D DCT and DST
373(4)
7.3 Homework problems
377(2)
8 The Walsh-Hadamard, slant, and Haar transforms
379(33)
8.1 The Walsh-Hadamard transform
379(13)
8.1.1 Hadamard matrix
379(2)
8.1.2 Hadamard-ordered Walsh-Hadamard transform (WHTh)
381(1)
8.1.3 Fast Walsh-Hadamard transform algorithm
382(2)
8.1.4 Sequency-ordered Walsh-Hadamard matrix (WHTw)
384(2)
8.1.5 Fast Walsh-Hadamard transform (sequency ordered)
386(6)
8.2 The slant transform
392(6)
8.2.1 Slant matrix
392(3)
8.2.2 Slant transform and its fast algorithm
395(3)
8.3 The Haar transform
398(10)
8.3.1 Continuous Haar transform
398(2)
8.3.2 Discrete Haar transform
400(3)
8.3.3 Computation of the discrete Haar transform
403(2)
8.3.4 Filter bank implementation
405(3)
8.4 Two-dimensional transforms
408(3)
8.5 Homework problems
411(1)
9 Karhunen-Loeve transform and principal component analysis
412(49)
9.1 Stochastic process and signal correlation
412(5)
9.1.1 Signals as stochastic processes
412(3)
9.1.2 Signal correlation
415(2)
9.2 Karhunen-Loeve transform (KLT)
417(21)
9.2.1 Continuous KLT
417(1)
9.2.2 Discrete KLT
418(1)
9.2.3 Optimalities of the KLT
419(4)
9.2.4 Geometric interpretation of the KLT
423(3)
9.2.5 Principal component analysis (PCA)
426(1)
9.2.6 Comparison with other orthogonal transforms
427(5)
9.2.7 Approximation of the KLT by the DCT
432(6)
9.3 Applications of the KLT
438(11)
9.3.1 Image processing and analysis
438(6)
9.3.2 Feature extraction for pattern classification
444(5)
9.4 Singular value decomposition transform
449(7)
9.4.1 Singular value decomposition
449(5)
9.4.2 Application in image compression
454(2)
9.5 Homework problems
456(5)
10 Continuous- and discrete-time wavelet transforms
461(31)
10.1 Why wavelet?
461(3)
10.1.1 Short-time Fourier transform and Gabor transform
461(1)
10.1.2 The Heisenberg uncertainty
462(2)
10.2 Continuous-time wavelet transform (CTWT)
464(4)
10.2.1 Mother and daughter wavelets
464(2)
10.2.2 The forward and inverse wavelet transforms
466(2)
10.3 Properties of the CTWT
468(3)
10.4 Typical mother wavelet functions
471(3)
10.5 Discrete-time wavelet transform (DTWT)
474(7)
10.5.1 Discretization of wavelet functions
474(2)
10.5.2 The forward and inverse transform
476(2)
10.5.3 A fast inverse transform algorithm
478(3)
10.6 Wavelet transform computation
481(3)
10.7 Filtering based on wavelet transform
484(6)
10.8 Homework problems
490(2)
11 Multiresolution analysis and discrete wavelet transform
492(54)
11.1 Multiresolution analysis (MRA)
492(26)
11.1.1 Scale spaces
492(6)
11.1.2 Wavelet spaces
498(3)
11.1.3 Properties of the scaling and wavelet filters
501(3)
11.1.4 Relationship between scaling and wavelet filters
504(2)
11.1.5 Wavelet series expansion
506(2)
11.1.6 Construction of scaling and wavelet functions
508(10)
11.2 Discrete wavelet transform (DWT)
518(5)
11.2.1 Discrete wavelet transform (DWT)
518(3)
11.2.2 Fast wavelet transform (FWT)
521(2)
11.3 Filter bank implementation of DWT and inverse DWT
523(12)
11.3.1 Two-channel filter bank and inverse DWT
523(7)
11.3.2 Two-dimensional DWT
530(5)
11.4 Applications in filtering and compression
535(7)
11.5 Homework problems
542(4)
Appendices
546(1)
A Review of linear algebra
546(10)
A.1 Basic definitions
546(5)
A.2 Eigenvalues and eigenvectors
551(1)
A.3 Hermitian matrix and unitary matrix
552(2)
A.4 Toeplitz and circulant matrices
554(1)
A.5 Vector and matrix differentiation
554(2)
B Review of random variables
556(9)
B.1 Random variables
556(2)
B.2 Multivariate random variables
558(4)
B.3 Stochastic models
562(3)
Bibliography 565(1)
Index 566
Ruye Wang is a Professor in the Engineering Department at Harvey Mudd College. Previously a Principal Investigator at the Jet Propulsion Laboratory, NASA, his research interests include image processing, computer vision, machine learning and remote sensing.