Explorations in Time-Frequency Analysis

✍ Scribed by Patrick Flandrin

• Publisher: Cambridge University Press
• Year: 2018
• Tongue: English
• Leaves: 231
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Computer Science, Computer Graphics, Image Processing and Robotics, Communications and Signal Processing, Engineering