Time Frequency Analysis (eBook)

Front Cover 1
Time Frequency Signal Analysis and Processing: A Comprehensive Reference 4
Copyright Page 5
Contents 10
Preface 8
List of Contributors 24
Part I: Introduction to the Concepts of TFSAP 28
Chapter 1. Time-Frequency Concepts 30
1.1 The Need for a Time-Frequency Distribution (TFD) 31
1.2 Signal Formulations and Characteristics in the (t, f ) Domain 39
1.3 Instantaneous Frequency and Time-Delay 46
1.4 Summary and Discussion 53
Chapter 2. Heuristic Formulation of Time-Frequency Distributions 56
2.1 Method 1: The Wigner-Ville Distribution 57
2.2 Method 2: Time-Varying Power Spectral Density 63
2.3 Method 3: Windowed FT (STFT, Spectrogram, Gabor Transform) 65
2.4 Method 4: Filtered Function of Time 69
2.5 Method 5: Instantaneous Power Spectra 70
2.6 Method 6: Energy Density 72
2.7 Relationship between TFDs 74
2.8 Summary and Discussion 79
Chapter 3. Theory of Quadratic TFDs 86
3.1 The WVD 87
3.2 Formulations of Quadratic TFDs 93
3.3 Properties of Quadratic TFDs 99
3.4 Summary, Discussion and Conclusions 103
Part II: Fundamental Principles of TFSAP 110
Chapter 4. Time-Frequency Signal and System Analysis 112
4.1 Analytic Signal & Instantaneous Frequency
4.2 Cross-terms & Localization in QuadraticTime-frequency Distributions
4.3 The Covariance Theory of Time-Frequency Analysis 129
4.4 Uncertainty in Time-Frequency Analysis 141
4.5 Generalized TFRs via Unitary Transforms 149
4.6 Signal Measures in the Time-Frequency Plane 155
4.7 Time-Frequency Transfer Function Calculus of Linear Time-Varying Systems 162
4.8 Wigner Distribution and Fractional Fourier Transform 172
4.9 Gabor Spectrogram 180
Chapter 5. Design of Time-Frequency Distributions 186
5.1 Ambiguity Functions 187
5.2 Reduced Interference Time-Frequency Distributions 195
5.3 Adaptive Time-Frequency Analysis 205
5.4 Polynomial Wigner-Ville Distributions 212
5.5 Design of Polynomial TFDs, with Applications 220
5.6 Time-Frequency Representations Covariant to Group Delay Shifts 230
5.7 Design of High-Resolution Quadratic TFDs with Separable Kernels 240
5.8 Fractional Fourier Transform and Generalized-Marginal TFDs 250
Part III: Time-Frequency Methods 256
Chapter 6. Implementation and Realization of TFDs 258
6.1 Discrete Time-Frequency Distributions 259
6.2 Quadratic and Higher Order Time-Frequency Analysis Based on the STFT 269
6.3 Gabor's Signal Expansion for a Non-Orthogonal Sampling Geometry 279
6.4 Spectrogram Decompositions of Time-Frequency Distributions 287
6.5 Computation of Discrete Quadratic TFDs 295
Chapter 7. Measures, Performance Assessment and Enhancement 306
7.1 Time-Frequency Analysis Based on the Affine Group 307
7.2 Time-Frequency Reassignment 317
7.3 Measuring Time-Frequency Distributions Concentration 324
7.4 Resolution Performance Assessment for Quadratic TFDs 332
7.5 Joint-Domain Representations via Discrete-Domain Frames 342
Chapter 8. Multi-Sensor and Time-Space Processing 350
8.1 Blind Source Separation Using Time-Frequency Distributions 351
8.2 Spatial Time-Frequency Distributions and Their Applications 361
8.3 Quadratic Detection in Arrays using TFDs 371
8.4 Implementation of STFDs-Based Source Separation Algorithms 376
8.5 Underdetermined Blind Source Separation for FM-like Signals 384
Part IV: Statistical Techniques 396
Chapter 9. Random Processes and Noise Analysis 398
9.1 Analysis of Noise in Time-Frequency Distributions 399
9.2 Statistical Processing of Dispersive Systems and Signals 409
9.3 Robust Time-Frequency Distributions 419
9.4 Time-Varying Power Spectra of Nonstationary Random Processes 427
9.5 Time-Frequency Characterization of Random Time-Varying Channels 437
Chapter 10. Instantaneous Frequency Estimation and Localization 448
10.1 Iterative Instantaneous Frequency Estimation for Random Signals 449
10.2 Adaptive Instantaneous Frequency Estimation Using TFDs 456
10.3 IF Estimation for Multicomponent Signals 464
10.4 Analysis of Polynomial FM Signals in Additive Noise 474
10.5 IF Estimation of FM Signals in Multiplicative Noise 484
Chapter 11. Time-Frequency Synthesis and Filtering 492
11.1 Linear Time-Frequency Filters 493
11.2 Time-Varying Filter via Gabor Expansion 503
11.3 Time-Frequency Filtering of Speech Signals in Hands-Free Telephone Systems 508
11.4 Signal Enhancement by Time-Frequency Peak Filtering 516
Chapter 12. Detection , Classification and Estimation 526
12.1 Optimal Time-Frequency Detectors 527
12.2 Time-Frequency Signal Analysis and Classification Using Matching Pursuits 537
12.3 System Identification using Time-Frequency Filtering 546
12.4 Time-Frequency Methods for Signal Estimation and Detection 555
Part V: Engineering Applications 566
Chapter 13. Time-Frequency Methods in Communications 568
13.1 Time-Frequency Interference Mitigation in Spread Spectrum Communication Systems 569
13.2 Communication Over Linear Dispersive Channels: A Time-Frequency Perspective 576
13.3 Eigenfunctions of Underspread Linear Communication Systems 585
13.4 Fractional Autocorrelation for Detection in Communications 595
Chapter 14. Time-Frequency Methods in Radar, Sonar & : Acoustics
14.1 Special Time-Frequency Analysis of Helicopter Doppler Radar Data 605
14.2 Time-Frequency Motion Compensation Algorithms for ISAR Imaging 617
14.3 Flight Parameter Estimation using Doppler and Lloyd's Mirror Effects 624
14.4 Wigner-Ville Analysis of High Frequency Radar Measurements 632
14.5 Time-Frequency Methods in Sonar 642
Chapter 15. Time-Frequency Diagnosis and Monitoring 654
15.1 Time-Frequency Analysis of Electric Power Disturbances 655
15.2 Combustion Diagnosis by TF Analysis of Car Engine Signals 662
15.3 Power Class Time-Frequency Representations and their Applications 670
15.4 Image Distortion Analysis using the Wigner-Ville Distribution 678
15.5 Time-Frequency Detection of EEG Abnormalities 690
15.6 Time-Frequency Based Machine Condition Monitoring and Fault Diagnsois 698
Chapter 16. Other Applications 710
Time-Frequency Bibliography 712
Time-Frequency Index 746