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E-raamat: Digital Signal Processing with Matlab Examples, Volume 2: Decomposition, Recovery, Data-Based Actions

Jose Maria Giron-Sierra

Formaat: EPUB+DRM
Sari: Signals and Communication Technology
Ilmumisaeg: 02-Dec-2016
Kirjastus: Springer Verlag, Singapore
Keel: eng
ISBN-13: 9789811025372

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Formaat: EPUB+DRM
Sari: Signals and Communication Technology
Ilmumisaeg: 02-Dec-2016
Kirjastus: Springer Verlag, Singapore
Keel: eng
ISBN-13: 9789811025372

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This is the second volume in a trilogy on modern Signal Processing. The three books provide a concise exposition of signal processing topics, and a guide to support individual practical exploration based on MATLAB programs.

This second book focuses on recent developments in response to the demands of new digital technologies. It is divided into two parts: the first part includes four chapters on the decomposition and recovery of signals, with special emphasis on images. In turn, the second part includes three chapters and addresses important data-based actions, such as adaptive filtering, experimental modeling, and classification.

Part I Decomposition and Recovery. Images

1 Filter Banks

(112)

1.1 Introduction

(1)

1.2 Filter Banks and Multirate Systems

(19)

1.2.1 Discrete Fourier Transforms

(4)

1.2.2 Modulated Filter Banks

(6)

1.2.3 Decimators and Interpolators

(3)

1.2.4 The Polyphase Representation

(5)

1.3 Symmetries and Filter Types

(16)

1.3.1 Linear Phase

(1)

1.3.2 FIR Filters with Linear Phase

(2)

1.3.3 Complementary Filters

(1)

1.3.4 Symmetries in the Frequency Response

(3)

1.3.5 Orthogonal FIR Filters

(2)

1.3.6 Mirror FIR Filters

(1)

1.3.7 Zeros of FIR Filters. Spectral Factorization

(5)

1.4 Two-Channel Filters and Perfect Reconstruction

(21)

1.4.1 Automatic Aliasing Cancellation, Perfect Reconstruction

(8)

1.4.2 Design Approaches for Two-Channel Filter Banks with PR

(11)

1.4.3 Conditions for Filters and Perfect Reconstruction

(2)

1.5 Aspects of Unity Gain Systems

(10)

1.5.1 Matrices of Interest

(4)

1.5.2 Allpass Filters

(2)

1.5.3 Lattice Structure

(1)

1.5.4 The Case of 2-Channel Filter Banks

(2)

1.6 Tree-Structured Filter Banks

(2)

1.7 Uniform M-Channel Filter Banks

(20)

1.7.1 Basic Equations

(2)

1.7.2 Paraunitary M-Channel Filter Banks

(1)

1.7.3 Cosine-Modulated Filter Banks

(4)

1.7.4 Linear-Phase Filter Banks

(13)

1.8 IIR Filter Banks

(9)

1.8.1 Orthogonal IIR Filter Banks

(2)

1.8.2 Linear Phase Orthogonal IIR Filter Banks

(1)

1.8.3 Implementation Aspects

(5)

1.9 Experiments

101

(9)

1.9.1 Perfect Reconstruction, Music

101

(2)

1.9.2 JPEG

103

(2)

1.9.3 Watermarking

105

(1)

1.9.4 Watermarking in Spectral Domain

105

(3)

1.9.5 Watermarking in Signal Domain

108

(2)

1.10 Resources

110

(5)

1.10.1 MATLAB

110

(1)

1.10.2 Internet

111

(1)

References

111

(4)

2 Wavelets

115

(128)

2.1 Introduction

115

(2)

2.2 An Important Example: The Haar Wavelets

117

(20)

2.2.1 Definitions

117

(2)

2.2.2 Multiresolution Analysis

119

(12)

2.2.3 Wavelets and Filter Banks

131

(6)

2.3 The Multiresolution Analysis Equation

137

(19)

2.3.1 Solving the MAE

137

(8)

2.3.2 Scaling Functions, Wavelets, and Function Expansions

145

(2)

2.3.3 Examples

147

(3)

2.3.4 Shannon Wavelets

150

(2)

2.3.5 Splines

152

(4)

2.4 Orthogonal Wavelets

156

(26)

2.4.1 Meyer Wavelet

157

(5)

2.4.2 Battle-Lemarie Wavelet

162

(4)

2.4.3 Daubechies Wavelets

166

(16)

2.5 Biorthogonal Wavelets

182

(14)

2.5.1 Daubechies Approach

184

(7)

2.5.2 More Ways to Find Biorthogonal Wavelets

191

(5)

2.6 Continuous Wavelets

196

(4)

2.6.1 The Mexican Hat Wavelet

196

(1)

2.6.2 The Morlet Wavelet

197

(2)

2.6.3 Complex B-Spline Wavelets

199

(1)

2.7 Continuous Wavelet Transform (CWT)

200

(2)

2.8 The Lifting Method and the Second Generation Wavelets

202

(15)

2.8.1 Example

206

(4)

2.8.2 Decomposition into Lifting Steps

210

(3)

2.8.3 Examples

213

(4)

2.9 More Analysis Flexibility

217

(6)

2.9.1 M-Band Wavelets

218

(1)

2.9.2 Wavelet Packets

219

(2)

2.9.3 Multiwavelets

221

(2)

2.10 Experiments

223

(7)

2.10.1 ECG Analysis Using the Morlet Wavelet

223

(3)

2.10.2 Signal Denoising

226

(1)

2.10.3 Compression

227

(3)

2.11 Applications

230

(2)

2.11.1 Earth Sciences

230

(1)

2.11.2 Medicine, Biology

231

(1)

2.11.3 Chemical

232

(1)

2.11.4 Industrial

232

(1)

2.12 The MATLAB Wavelet Toolbox

232

(4)

2.12.1 1-D Continuous Wavelet

233

(1)

2.12.2 1-D Discrete Wavelet

233

(2)

2.12.3 Wavelet Packets

235

(1)

2.12.4 Lifting

235

(1)

2.13 Resources

236

(7)

2.13.1 MATLAB

236

(1)

2.13.2 Internet

237

(1)

References

238

(5)

3 Image and 2D Signal Processing

243

(102)

3.1 Introduction

243

(1)

3.2 Image Files and Display

243

(3)

3.2.1 Image Files

244

(1)

3.2.2 Image Display with MATLAB

244

(2)

3.3 Basic Image Analysis and Filtering

246

(8)

3.3.1 Histograms

246

(1)

3.3.2 Histogram Equalization

247

(1)

3.3.3 Image Adjust

248

(1)

3.3.4 2D Filtering with Neighbours

249

(2)

3.3.5 Gaussian 2D Filters

251

(3)

3.3.6 Picture Sharpening

254

(1)

3.4 2D Fourier Transform

254

(4)

3.4.1 2D Fourier Transform of Edges

255

(2)

3.4.2 2D Fourier Transform of a Picture

257

(1)

3.5 Filtering with the 2D Fourier Transform

258

(12)

3.5.1 Basic Low Pass and High Pass Filtering using 2D DFT

259

(3)

3.5.2 Other Low Pass Filters Using 2D DFT

262

(3)

3.5.3 Other High-Pass Filters Using 2D DFT

265

(5)

3.6 Edges

270

(3)

3.6.1 Thresholding

270

(1)

3.6.2 Edges

271

(2)

3.7 Color Images

273

(17)

3.7.1 RGB Example

283

(2)

3.7.2 HSV Example

285

(2)

3.7.3 YIQ Example

287

(2)

3.7.4 Indexed Images

289

(1)

3.8 Hough Transform and Radon Transform

290

(17)

3.8.1 The Sinogram

290

(2)

3.8.2 The Hough Transform

292

(4)

3.8.3 The Radon Transform, and Computerized Tomography

296

(9)

3.8.4 IPT Functions for the Radon Transform

305

(2)

3.9 Filter Banks and Images

307

(27)

3.9.1 Initial Overview

307

(19)

3.9.2 Design of 2D Filters

326

(8)

3.10 Nonequispaced Data and the Fourier Transform

334

(4)

3.10.1 Fourier Transform Versions for the Polar Context

334

(1)

3.10.2 Nonequispaced Fourier Transform

335

(3)

3.11 Experiments

338

(4)

3.11.1 Capturing Images with a Webcam

338

(2)

3.11.2 Backprojection Steps

340

(2)

3.12 Resources

342

(3)

3.12.1 MATLAB

342

(1)

3.12.2 Internet

342

(1)

References

342

(3)

4 Wavelet Variants for 2D Analysis

345

(126)

4.1 Introduction

345

(1)

4.2 Laplacian Pyramid

345

(5)

4.3 Steerable Filters and Pyramids

350

(18)

4.3.1 Steerable Filters

351

(10)

4.3.2 Steerable Pyramid

361

(7)

4.4 Application of Wavelets to Images

368

(18)

4.4.1 Application to a Test Image

369

(6)

4.4.2 Application to a Photograph

375

(3)

4.4.3 Some Wavelet-Based Algorithms for Image Coding and Compression

378

(8)

4.5 New Wavelets for Images

386

(45)

4.5.1 Perspective

387

(1)

4.5.2 Wedgelets

388

(4)

4.5.3 Ridgelets and First Generation Curvelets

392

(5)

4.5.4 Curvelets (Second Generation)

397

(7)

4.5.5 Contourlets

404

(5)

4.5.6 Bandelets

409

(13)

4.5.7 Shearlets

422

(5)

4.5.8 Other Wavelet Variants

427

(4)

4.6 Complex Wavelets

431

(10)

4.6.1 Implementation Issues

433

(4)

4.6.2 2-D Application

437

(4)

4.7 Experiments

441

(7)

4.7.1 2 Level Haar Decomposition of the Image

441

(1)

4.7.2 Fine Noise Is Added. Denoising Is Applied

441

(2)

4.7.3 Patched Noise Is Added. Denoising Is Applied

443

(1)

4.7.4 Display of LL Regions, No Noise

444

(4)

4.8 Applications

448

(7)

4.8.1 Denoising

449

(2)

4.8.2 Compression

451

(1)

4.8.3 Image Registration

452

(2)

4.8.4 Seismic Signals

454

(1)

4.8.5 Other Applications

454

(1)

4.9 Resources

455

(16)

4.9.1 MATLAB

455

(2)

4.9.2 Internet

457

(2)

References

459

(12)

Part II Data-Based Actions: Adaptive Filtering, Modelling, Analysis, and Classification

5 Adaptive Filters and Observers

471

(110)

5.1 Introduction

471

(1)

5.2 The Wiener Filter

472

(21)

5.2.1 Problem Statement. Transfer Function

473

(5)

5.2.2 Versions of the Filter

478

(8)

5.2.3 Spectral Factorization

486

(2)

5.2.4 The Error Surface

488

(3)

5.2.5 A Simple Example of Batch Mode and Recursive Mode

491

(2)

5.3 Recursive Estimation of Filter Coefficients

493

(12)

5.3.1 The RLS Method

494

(4)

5.3.2 Search-Based Methods

498

(7)

5.4 Adaptive Filters

505

(12)

5.4.1 System Identification

506

(2)

5.4.2 Inverse System Identification

508

(3)

5.4.3 Noise Cancellation

511

(4)

5.4.4 Linear Prediction

515

(2)

5.5 Image Deblurring

517

(8)

5.5.1 Motion blur

522

(3)

5.6 More Adaptive Filters and Some Mathematical Aspects

525

(20)

5.6.1 LMS Variants

525

(4)

5.6.2 Other Adaptive Filters

529

(1)

5.6.3 Mathematical Aspects

529

(14)

5.6.4 Unifying Perspective

543

(2)

5.7 Bayesian Estimation: Application to Images

545

(19)

5.7.1 Introduction to Image Restoration

547

(1)

5.7.2 Uniform Out-of-Focus Blur

548

(1)

5.7.3 Atmospheric Turbulence Blur

548

(1)

5.7.4 Linear Motion Blur

549

(1)

5.7.5 The Lucy-Richardson Algorithm (RLA)

550

(4)

5.7.6 Other Aspects of the Topic

554

(10)

5.8 Observers

564

(5)

5.8.1 The Luenberger Observer

564

(4)

5.8.2 Noises

568

(1)

5.9 Experiments

569

(5)

5.9.1 Eigenvalues of Signals

569

(3)

5.9.2 Water

572

(1)

5.9.3 Fetal Heart Rate Monitoring

573

(1)

5.10 Some Motivating Applications

574

(2)

5.11 Resources

576

(5)

5.11.1 MATLAB

576

(1)

5.11.2 Internet

577

(1)

References

578

(3)

6 Experimental Modelling

581

(66)

6.1 Introduction

581

(1)

6.2 Data Fitting

582

(3)

6.3 Coherence. Delays

585

(9)

6.3.1 Coherence Between Two Signals

586

(1)

6.3.2 Delays

587

(7)

6.4 Basic Experimental Transfer Function Modelling

594

(13)

6.4.1 Two Simple Transfer Function Examples

594

(3)

6.4.2 Obtaining a Transfer Function Model from Impulse Response

597

(3)

6.4.3 Obtaining a Transfer Function Model from Sine Sweep

600

(3)

6.4.4 Obtaining a Transfer Function Model from Response to Noise

603

(4)

6.5 The Case of Transfer Functions with Delay

607

(10)

6.5.1 Two Simple Examples

607

(1)

6.5.2 Responses of Case 1d

608

(3)

6.5.3 Responses of Case 2d

611

(2)

6.5.4 Detecting the Delay

613

(1)

6.5.5 Getting Strange Models

614

(3)

6.6 Methods for Frequency-Domain Modelling

617

(5)

6.6.1 The Levi's Approximation

618

(2)

6.6.2 The SK Iterative Weighted Approach

620

(1)

6.6.3 The Vector Fitting (VF) Approach

620

(2)

6.7 Methods for Time-Series Modelling

622

(6)

6.7.1 Basic Identification Methods

624

(2)

6.7.2 Variants of Recursive Parameter Estimation

626

(2)

6.8 Experiments

628

(7)

6.8.1 AR Model Identification of Canadian Lynx Data

628

(2)

6.8.2 Model Order

630

(5)

6.9 Introduction to the MATLAB System Identification Toolbox

635

(7)

6.9.1 Identification Steps Using the Toolbox Functions

635

(2)

6.9.2 Using the GUI

637

(5)

6.10 Resources

642

(5)

6.10.1 MATLAB

642

(1)

6.10.2 Internet

643

(1)

References

643

(4)

7 Data Analysis and Classification

647

(190)

7.1 Introduction

647

(1)

7.2 A Basic Idea of Component Analysis

648

(3)

7.3 Principal Component Analysis (PCA)

651

(14)

7.3.1 Mathematical Aspects

652

(3)

7.3.2 Principal Components

655

(4)

7.3.3 Application Examples

659

(6)

7.4 Independent Component Analysis (ICA)

665

(46)

7.4.1 Blind Source Separation and the Cocktail Party Problem

665

(3)

7.4.2 PCA and ICA

668

(2)

7.4.3 Whitening

670

(9)

7.4.4 Determination of Non-Gaussianity

679

(11)

7.4.5 Assumptions of the ICA Method. Independence

690

(3)

7.4.6 Contrast Functions

693

(1)

7.4.7 Optimization Algorithms

694

(10)

7.4.8 Application Examples

704

(7)

7.5 Clusters. Discrimination

711

(37)

7.5.1 Discrimination

714

(7)

7.5.2 Clustering

721

(7)

7.5.3 Kernels

728

(15)

7.5.4 Other Approaches

743

(5)

7.6 Classification and Probabilities

748

(31)

7.6.1 The Expectation-Maximization Algorithm (EM)

749

(4)

7.6.2 Naive Bayes Classifier

753

(2)

7.6.3 Quadratic Discriminant Analysis (QDA)

755

(2)

7.6.4 Logistic Discriminantion

757

(1)

7.6.5 Bayesian Linear Regression. Prediction

758

(6)

7.6.6 Sets of Random Variables. Kriging

764

(8)

7.6.7 Gaussian Processes (GP)

772

(7)

7.7 Entropy, Divergence, and Related Aspects

779

(6)

7.7.1 Entropy

779

(1)

7.7.2 Divergence

780

(2)

7.7.3 Jensen's Inequality

782

(1)

7.7.4 Variational Bayes Methodology

783

(2)

7.8 Neurons

785

(11)

7.8.1 The Perceptron

786

(3)

7.8.2 The Adaline

789

(1)

7.8.3 Multilayer Neural Networks

790

(6)

7.9 Experiments

796

(19)

7.9.1 Face Detection

796

(15)

7.9.2 Color Reduction Using K-Means

811

(4)

7.10 Some Pointers to Related Topics

815

(3)

7.11 Resources

818

(19)

7.11.1 MATLAB

818

(2)

7.11.2 Internet

820

(2)

References

822

(15)

Appendix: Long Programs

837

(72)

Index

909

Prof. Jose M. Giron-Sierra was born in Valladolid, Spain. He received his Ph.D. in Physics in 1978, Universidad Complutense de Madrid, Spain. Prof. Giron-Sierra wrote more than 160 publications in various international journals. He is IEEE, AIAA, and Eurosim member and belongs to two IFAC Technical Committees.

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E-raamat: Digital Signal Processing with Matlab Examples, Volume 2: Decomposition, Recovery, Data-Based Actions

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