Explorations in Time-Frequency Analysis

An authoritative exposition of the methods at the heart of modern non-stationary signal processing from a recognised leader in the field. Offering a global view that favours interpretations and historical perspectives, it explores the basic concepts of time-frequency analysis, and examines the most recent results and developments in the field in the context of existing, lesser-known approaches. Several example waveform families from bioacoustics, mathematics and physics are examined in detail, with the methods for their analysis explained using a wealth of illustrative examples. Methods are discussed in terms of analysis, geometry and statistics. This is an excellent resource for anyone wanting to understand the 'why and how' of important methodological developments in time-frequency analysis, including academics and graduate students in signal processing and applied mathematics, as well as application-oriented scientists.

1. Introduction; Part I. Basics and Constraints: 2. Small data are beautiful; 3. Of signals and noise; 4. On time, frequency, and Gauss; 5. Uncertainty; 6. From time and frequency to time-frequency; 7. Uncertainty revisited; 8. On stationarity; Part II. Geometry and Statistics: 9. Spectrogram geometry 1; 10. Sharpening spectrograms; 11. A digression on Hilbert-Huang transform; 12. Spectrogram geometry 2; 13. The noise case; 14. More on maxima; 15. More on zeros; 16. Back to examples; 17. Conclusion; 18. Annex – software tools.

Patrick Flandrin holds a Research Director position at the CNRS (Centre National de la Recherche Scientifique), working in the Laboratoire de Physique of the École normale supérieure de Lyon. He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and European Association for Signal Processing (EURASIP), and a Member of the French Academy of Sciences.