Explorations in Time-Frequency Analysis

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. Cover......Page 1 Front Matter ......Page 2 Explorations in Time-Frequency Analysis......Page 4 Copyright ......Page 5 Dedication ......Page 6 Contents ......Page 8 Acknowledgments......Page 11 Preface......Page 14 Notation......Page 16 1 Introduction......Page 18 Part I: Basics and Constraints ......Page 24 2 Small Data Are Beautiful......Page 26 3 Of Signals and Noise......Page 38 4 On Time, Frequency, and Gauss......Page 46 5 Uncertainty......Page 52 6 From Time and Frequency to Time-Frequency......Page 57 7 Uncertainty Revisited......Page 67 8 On Stationarity......Page 73 Part II: Geometry and Statistics ......Page 84 9 Spectrogram Geometry 1......Page 86 10 Sharpening Spectrograms......Page 94 11 A Digression on the Hilbert–Huang Transform......Page 115 12 Spectrogram Geometry 2......Page 123 13 The Noise Case......Page 133 14 More on Maxima......Page 141 15 More on Zeros......Page 156 16 Back to Examples......Page 185 17 Conclusion......Page 214 18 Annex: Software Tools......Page 216 References......Page 218 Index......Page 227