Details

Autor(en) / Beteiligte

• Hlawatsch, F
• Auger, Francois

Titel

Time-frequency analysis : concepts and methods

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references and index.
• Time-Frequency Analysis; Contents; Preface; First part. Fundamental Concepts and Methods; Chapter 1. Time-Frequency Energy Distributions: An Introduction; 1.1. Introduction; 1.2. Atoms; 1.3. Energy; 1.3.1. Distributions; 1.3.2. Devices; 1.3.3. Classes; 1.4. Correlations; 1.5. Probabilities; 1.6. Mechanics; 1.7. Measurements; 1.8. Geometries; 1.9. Conclusion; 1.10. Bibliography; Chapter 2. Instantaneous Frequency of a Signal; 2.1. Introduction; 2.2. Intuitive approaches; 2.3. Mathematical definitions; 2.3.1. Ambiguity of the problem; 2.3.2. Analytic signal and Hilbert transform
• 2.3.3. Application to the definition of instantaneous frequency2.3.4. Instantaneous methods; 2.4. Critical comparison of the different definitions; 2.4.1. Interest of linear filtering; 2.4.2. Bounds of the quantities introduced; 2.4.3. Instantaneous nature; 2.4.4. Interpretation by the average; 2.5. Canonical pairs; 2.6. Phase signals; 2.6.1. Blaschke factors; 2.6.2. Oscillatory singularities; 2.7. Asymptotic phase signals; 2.7.1. Parabolic chirp; 2.7.2. Cubic chirp; 2.8. Conclusions; 2.9. Bibliography; Chapter 3. Linear Time-Frequency Analysis I: Fourier-Type Representations
• 3.1. Introduction3.2. Short-time Fourier analysis; 3.2.1. Short-time Fourier transform; 3.2.2. Time-frequency energy maps; 3.2.3. Role of the window; 3.2.4. Reconstruction/synthesis; 3.2.5. Redundancy; 3.3. Gabor transform; Weyl-Heisenberg and Wilson frames; 3.3.1. Sampling of the short-time Fourier transform; 3.3.2. Weyl-Heisenberg frames; 3.3.3. Zak transform and "critical" Weyl-Heisenberg frames; 3.3.4. Balian-Low theorem; 3.3.5. Wilson bases and frames, local cosine bases; 3.4. Dictionaries of time-frequency atoms; adaptive representations
• 3.4.1. Multi-scale dictionaries of time-frequency atoms3.4.2. Pursuit algorithm; 3.4.3. Time-frequency representation; 3.5. Applications to audio signals; 3.5.1. Analysis of superimposed structures; 3.5.2. Analysis of instantaneous frequency variations; 3.5.3. Transposition of an audio signal; 3.6. Discrete algorithms; 3.6.1. Fast Fourier transform; 3.6.2. Filter banks: fast convolution; 3.6.3. Discrete short-time Fourier transform; 3.6.4. Discrete Gabor transform; 3.7. Conclusion; 3.8. Acknowledgements; 3.9. Bibliography
• Chapter 4. Linear Time-Frequency Analysis II: Wavelet-Type Representations4.1. Introduction: scale and frequency; 4.2. Continuous wavelet transform; 4.2.1. Analysis and synthesis; 4.2.2. Multiscale properties; 4.3. Discrete wavelet transform; 4.3.1. Multi-resolution analysis; 4.3.2. Mallat algorithm; 4.3.3. Graphical representation; 4.4. Filter banks and wavelets; 4.4.1. Generation of regular scaling functions; 4.4.2. Links with approximation theory; 4.4.3. Orthonormality and bi-orthonormality/perfect reconstruction; 4.4.4. Polyphase matrices and implementation
• 4.4.5. Design of wavelet filters with finite impulse response
• 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.
• English