Book contents
- Frontmatter
- Dedication
- Contents
- Acknowledgements
- Preface
- Notation
- 1 Introduction
- Part I Basics and Constraints
- Part II Geometry and Statistics
- 9 Spectrogram Geometry 1
- 10 Sharpening Spectrograms
- 11 A Digression on the 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
- References
- Index
10 - Sharpening Spectrograms
from Part II - Geometry and Statistics
Published online by Cambridge University Press: 22 August 2018
- Frontmatter
- Dedication
- Contents
- Acknowledgements
- Preface
- Notation
- 1 Introduction
- Part I Basics and Constraints
- Part II Geometry and Statistics
- 9 Spectrogram Geometry 1
- 10 Sharpening Spectrograms
- 11 A Digression on the 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
- References
- Index
Summary
Time-frequency energy distributions are faced with a trade-off between localization and interference. Different approaches exist for getting sharply localized that are almost interference-free: they are based either on some forms of post-processing (reassignment and synchrosqueezing, and variations thereof, which both move computed values in the plane) or by invoking sparsity arguments and replacing a Fourier-based transform by a constrained optimization. When targeting a sharpened distribution, another trade-off exists between localization and reconstruction capabilities: some methods are presented in order to overcome this limitation.
- Type
- Chapter
- Information
- Explorations in Time-Frequency Analysis , pp. 77 - 97Publisher: Cambridge University PressPrint publication year: 2018