Practical Time-Frequency Analysis: Gabor and Wavelet Transforms, with an Implementation in S
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Table of contents
- Title Page3
- Copyright Page4
- Contents11
- Part I: Background Material25
- Chapter 1. Time, Frequency, and Time-Frequency27
- 1.1 First Integral Transforms and Function Spaces27
- 1.2 Sampling and Aliasing36
- 1.3 Wiener's Deterministic Spectral Theory41
- 1.4 Deterministic Spectral Theory for Time Series44
- 1.5 Time-Frequency Representations52
- 1.6 Examples and S-Commands63
- 1.7 Notes and Complements64
- Chapter 2. Spectral Theory of Stationary Random Processes: A Primer67
- 2.1 Stationary Processes67
- 2.2 Spectral Representations74
- 2.3 Nonparametric Spectral Estimation79
- 2.4 Spectral Estimation in Practice84
- 2.5 Examples and S-Commands89
- 2.6 Notes and Complements97
- Part II: Gabor and Wavelet Transforms99
- Chapter 3. The Continuous Gabor Transform101
- 3.1 Definitions and First Properties101
- 3.2 Commonly Used Windows106
- 3.3 Examples109
- 3.4 Examples and S-Commands122
- 3.5 Notes and Complements127
- Chapter 4. The Continuous Wavelet Transform129
- 4.1 Definitions and Basic Properties129
- 4.2 Continuous Multiresolutions136
- 4.3 Commonly Used Analyzing Wavelets137
- 4.4 Wavelet Singularity Analysis141
- 4.5 First Examples of Wavelet Analyses146
- 4.6 Examples and S-Commands157
- 4.7 Notes and Complements160
- Chapter 5. Discrete Time-Frequency Transforms and Algorithms163
- 5.1 Frames164
- 5.2 Intermediate Discretization: The Dyadic Wavelet Transform172
- 5.3 Matching Pursuit179
- 5.4 Wavelet Orthonormal Bases183
- 5.5 Playing with Time-Frequency Localization196
- 5.6 Algorithms and Implementation203
- 5.7 Examples and S-Commands212
- 5.8 Notes and Complements215
- Part III: Signal Processing Applications219
- Chapter 6. Time-Frequency Analysis of Stochastic Processes221
- 6.1 Second-Order Processes221
- 6.2 Time-Frequency Analysis of Stationary Processes232
- 6.3 First Steps toward Non-stationarity248
- 6.4 Examples and S-Commands262
- 6.5 Notes and Complements268
- Chapter 7. Analysis of Frequency Modulated Signals271
- 7.1 Asymptotic Signals272
- 7.2 Generalities on Asymptotic Signals276
- 7.3 Ridge and Local Extrema286
- 7.4 Algorithms for Ridge Estimation291
- 7.5 The "Crazy Climbers" Algorithm298
- 7.6 Reassignment Methods303
- 7.7 Examples and S-Commands307
- 7.8 Notes and Complements308
- Chapter 8. Statistical Reconstructions309
- 8.1 Nonparametric Regression309
- 8.2 Regression by Thresholding311
- 8.3 The Smoothing Spline Approach314
- 8.4 Reconstruction from the Extrema of the Dyadic Wavelet Transform318
- 8.5 Reconstruction from Ridge Skeletons328
- 8.6 Examples and S-Commands346
- 8.7 Notes and Complements352
- Part IV: The Swave Library355
- Chapter 9. Downloading and Installing the Swave Package357
- 9.1 Downloading Swave357
- 9.2 Installing Swave on a Unix Platform358
- 9.3 Troubleshooting358
- Chapter 10. The Swave S Functions361
- Chapter 11. The Swave S Utilities409
- Bibliographies439
- General References441
- Wavelet Books465
- Splus Books469
- Indexes471
- Notation Index473
- Author Index477
- S Functions and Utilities481
- Subject Index483
Time frequency analysis has been the object of intense research activity in the last decade. This book gives a self-contained account of methods recently introduced to analyze mathematical functions and signals simultaneously in terms of time and frequency variables. The book gives a detailed presentation of the applications of these transforms to signal processing, emphasizing the continuous transforms and their applications to signal analysis problems, including estimation, denoising, detection, and synthesis. To help the reader perform these analyses, Practical Time-Frequency Analysis provides a set of useful tools in the form of a library of S functions, downloadable from the authors' Web sites in the United States and France.
Key Features
* Detailed presentation of the Wavelet and Gabor transforms
* Applications to deterministic and random signal theory
* Spectral analysis of nonstationary signals and processes
* Numerous practical examples ranging from speech analysis to underwater acoustics, earthquake engineering, internet traffic, radar signal denoising, medical data interpretation, etc
* Accompanying software and data sets, freely downloadable from the book's Web page
Key Features
* Detailed presentation of the Wavelet and Gabor transforms
* Applications to deterministic and random signal theory
* Spectral analysis of nonstationary signals and processes
* Numerous practical examples ranging from speech analysis to underwater acoustics, earthquake engineering, internet traffic, radar signal denoising, medical data interpretation, etc
* Accompanying software and data sets, freely downloadable from the book's Web page