Practical Time-Frequency Analysis (eBook)

Front Cover 1
Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S 4
Copyright Page 5
Contents 12
Part I: Background Material 26
Chapter 1. Time, Frequency, and Time-Frequency 28
1.1 First Integral Transforms and Function Spaces 28
1.2 Sampling and Aliasing 37
1.3 Wiener's Deterministic Spectral Theory 42
1.4 Deterministic Spectral Theory for Time Series 45
1.5 Time-Frequency Representations 53
1.6 Examples and S-Commands 64
1.7 Notes and Complements 65
Chapter 2. Spectral Theory of Stationary Random Processes: A Primer 68
2.1 Stationary Processes 68
2.2 Spectral Representations 75
2.3 Nonparametric Spectral Estimation 80
2.4 Spectral Estimation in Practice 85
2.5 Examples and S-Commands 90
2.6 Notes and Complements 98
Part II: Gabor and Wavelet Transforms 100
Chapter 3. The Continuous Gabor Transform 102
3.1 Definitions and First Properties 102
3.2 Commonly Used Windows 107
3.3 Examples 110
3.4 Examples and S-Commands 123
3.5 Notes and Complements 128
Chapter 4. The Continuous Wavelet Transform 130
4.1 Definitions and Basic Properties 130
4.2 Continuous Multiresolutions 137
4.3 Commonly Used Analyzing Wavelets 138
4.4 Wavelet Singularity Analysis 142
4.5 First Examples of Wavelet Analyses 147
4.6 Examples and S-Commands 158
4.7 Notes and Complements 161
Chapter 5. Discrete Time-Frequency Transforms and Algorithms 164
5.1 Frames 165
5.2 Intermediate Discretization: The Dyadic Wavelet Transform 173
5.3 Matching Pursuit 180
5.4 Wavelet Orthonormal Bases 184
5.5 Playing with Time-Frequency Localization 197
5.6 Algorithms and Implementation 204
5.7 Examples and S-Commands 213
5.8 Notes and Complements 216
Part III: Signal Processing Applications 220
Chapter 6. Time-Frequency Analysis of Stochastic Processes 222
6.1 Second-Order Processes 222
6.2 Time-Frequency Analysis of Stationary Processes 233
6.3 First Steps toward Non-stationarity 249
6.4 Examples and S-Commands 263
6.5 Notes and Complements 269
Chapter 7. Analysis of Frequency Modulated Signals 272
7.1 Asymptotic Signals 273
7.2 Generalities on Asymptotic Signals 277
7.3 Ridge and Local Extrema 287
7.4 Algorithms for Ridge Estimation 292
7.5 The "Crazy Climbers" Algorithm 299
7.6 Reassignment Methods 304
7.7 Examples and S-Commands 308
7.8 Notes and Complements 309
Chapter 8. Statistical Reconstructions 310
8.1 Nonparametric Regression 310
8.2 Regression by Thresholding 312
8.3 The Smoothing Spline Approach 315
8.4 Reconstruction from the Extrema of the Dyadic Wavelet Transform 319
8.5 Reconstruction from Ridge Skeletons 329
8.6 Examples and S-Commands 347
8.7 Notes and Complements 353
Part IV: The Swave Library 356
Chapter 9. Downloading and Installing the Swave Package 358
9.1 Downloading Swave 358
9.2 Installing Swave on a Unix Platform 359
9.3 Troubleshooting 359
Chapter 10. The Swave S Functions 362
Chapter 11. The Swave S Utilities 410
Bibliographies 440
General References 442
Wavelet Books 466
Splus Books 470
Indexes 472
Notation Index 474
Author Index 478
S Functions and Utilities 482
Subject Index 484