Table Of Content

Half-title Page: i Title page Page: iii Copyright information Page: iv Dedication Page: v Table of contents Page: vii Acknowledgments Page: x Preface Page: xiii Notation Page: xv 1 Introduction Page: 1 Part I Basics and Constraints Page: 7 2 Small Data Are Beautiful Page: 9 2.1 Gravitational Waves Page: 9 2.2 Bats Page: 11 2.3 Riemann-Like Special Functions Page: 14 2.4 Chirps (Everywhere) Page: 16 3 Of Signals and Noise Page: 21 3.1 Order versus Disorder Page: 21 3.2 Signals Page: 22 3.3 Noise Page: 24 4 On Time, Frequency, and Gauss Page: 29 4.1 Gauss Page: 29 4.2 From Gauss to Fourier Page: 31 4.3 From Gauss to Shannon-Nyquist Page: 31 4.4 From Gauss to Gabor Page: 32 5 Uncertainty Page: 35 5.1 Variance Page: 35 5.2 Entropy Page: 38 5.3 Ubiquity and Interpretation Page: 39 6 From Time and Frequency to Time-Frequency Page: 40 6.1 Correlation and Ambiguity Page: 40 6.2 Distribution and Wigner Page: 43 6.3 Spectrograms, Cohen, and the Like Page: 46 7 Uncertainty Revisited Page: 50 7.1 L[sub(2)]-Norm Page: 50 7.2 L[sub(p)]-Norms and Entropy Page: 51 7.3 Concentration and Support Page: 51 7.4 Variance Page: 53 7.5 Uncertainty and Time-Frequency Localization Page: 54 8 On Stationarity Page: 56 8.1 Relative Stationarity Page: 57 8.2 Testing Stationarity Page: 60 Part II Geometry and Statistics Page: 67 9 Spectrogram Geometry 1 Page: 69 9.1 One Logon Page: 69 9.2 Two Logons Page: 70 9.3 Many Logons and Voronoi Page: 73 10 Sharpening Spectrograms Page: 77 10.1 Reassignment Page: 78 10.2 Multitaper Reassignment Page: 83 10.3 Synchrosqueezing Page: 88 10.4 Sparsity Page: 90 10.5 Wedding Sharpening and Reconstruction Page: 96 11 A Digression on the Hilbert–Huang Transform Page: 98 11.1 Empirical Mode Decomposition Page: 98 11.2 Huang's Algorithm Page: 100 11.3 The Hilbert–Huang Transform Page: 100 11.4 Pros, Cons, and Variations Page: 101 12 Spectrogram Geometry 2 Page: 106 12.1 Spectrogram, STFT, and Bargmann Page: 106 12.2 Reassignment Variations Page: 107 12.3 Attractors, Basins, Repellers, and Contours Page: 111 13 The Noise Case Page: 116 13.1 Time-Frequency Patches Page: 116 13.2 Correlation Structure Page: 118 13.3 Logon Packing Page: 121 14 More on Maxima Page: 124 14.1 A Randomized Lattice Model Page: 124 14.2 Ordinates and Maxima Distributions Page: 129 14.3 Voronoi Page: 134 15 More on Zeros Page: 139 15.1 Factorizations Page: 139 15.2 Density Page: 143 15.3 Pair Correlation Function Page: 144 15.4 Voronoi Page: 145 15.5 Delaunay Page: 149 15.6 Signal Extraction from “Silent” Points Page: 153 15.7 Universality Page: 161 15.8 Singularities and Phase Dislocations Page: 164 16 Back to Examples Page: 168 16.1 Gravitational Waves Page: 168 16.2 Bats Page: 175 16.3 Riemann-Like Special Functions Page: 188 17 Conclusion Page: 197 18 Annex: Software Tools Page: 199 References Page: 201 Index Page: 210

Description:

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.