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Informationen zum Autor Franz Hlawatsch is an Associate Professor at the Vienna University of Technology, Austria. His research interests are in the areas of time-frequency signal processing, non-stationary statistical signal processing and wireless communications. Francois Auger is Head of the Physical Measurements Department of the Technology Institute of the University of Saint Nazaire, France. His current research interests include motor control, embedded control and signal processing with FPGAs, spectral estimation and time-frequency representations. Klappentext Covering a period of about 25 years, during which time-frequency has undergone significant developments, this book is principally addressed to researchers and engineers interested in non-stationary signal analysis and processing. It is written by recognized experts in the field. Zusammenfassung Covering a period of about 25 years! during which time-frequency has undergone significant developments! this book is principally addressed to researchers and engineers interested in non-stationary signal analysis and processing. It is written by recognized experts in the field. Inhaltsverzeichnis Preface 13 FIRST PART. FUNDAMENTAL CONCEPTS AND METHODS 17 Chapter 1. Time-Frequency Energy Distributions: An Introduction 19 Patrick FLANDRIN 1.1. Introduction 19 1.2. Atoms 20 1.3. Energy 21 1.3.1. Distributions 22 1.3.2. Devices 22 1.3.3. Classes 23 1.4. Correlations 26 1.5. Probabilities 27 1.6. Mechanics 29 1.7. Measurements 29 1.8. Geometries 32 1.9. Conclusion 33 1.10.Bibliography 34 Chapter 2. Instantaneous Frequency of a Signal 37 Bernard PICINBONO 2.1. Introduction 37 2.2. Intuitive approaches 38 2.3. Mathematical definitions 40 2.3.1. Ambiguity of the problem 40 2.3.2. Analytic signal and Hilbert transform 40 2.3.3. Application to the definition of instantaneous frequency 42 2.3.4. Instantaneous methods 45 2.4. Critical comparison of the different definitions 46 2.4.1. Interest of linear filtering 46 2.4.2. Bounds of the quantities introduced 46 2.4.3. Instantaneous nature 47 2.4.4. Interpretation by the average 48 2.5. Canonical pairs 49 2.6. Phase signals 50 2.6.1. Blaschke factors 50 2.6.2. Oscillatory singularities 54 2.7. Asymptotic phase signals 57 2.7.1. Parabolic chirp 57 2.7.2. Cubic chirp 59 2.8. Conclusions 59 2.9. Bibliography 60 Chapter 3. Linear Time-Frequency Analysis I: Fourier-Type Representations 61 Remi GRIBONVAL 3.1. Introduction 61 3.2. Short-time Fourier analysis 62 3.2.1. Short-time Fourier transform 63 3.2.2. Time-frequency energy maps 64 3.2.3. Role of the window 66 3.2.4. Reconstruction/synthesis 71 3.2.5. Redundancy 71 3.3. Gabor transform; Weyl-Heisenberg and Wilson frames 71 3.3.1. Sampling of the short-time Fourier transform 71 3.3.2. Weyl-Heisenberg frames 72 3.3.3. Zak transform and "critical" Weyl-Heisenberg frames 74 3.3.4. Balian-Low theorem 75 3.3.5. Wilson bases and frames, local cosine bases 75 3.4. Dictionaries of time-frequency atoms; adaptive representations 77 3.4.1. Multi-scale dictionaries of time-frequency atoms 77 3.4.2. Pursuit algorithm 78 3.4.3. Time-frequency representation 79 3.5. Applications to audio signals 80 3.5.1. Analysis of superimposed structures 80 3.5.2. Analysis of instantaneous frequency variations 80 3.5.3. Transposition of an audio signal 82 3.6. Discrete algorithms 82 3.6.1. Fast Fourier transform 83 3.6.2. Filter banks: fast convolution ...
