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
15 - More on Zeros
from Part II - Geometry and Statistics
Published online by Cambridge University Press: 22 August 2018
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
Summary
Thanks to its Bargmann representation, a Gaussian STFT can be factorized so as to be described by its zeros. This paves the way for a new approach that exploits the (usually ignored) zeros of the transform. Zeros can serve as centers for Voronoi cells whose statistics is investigated in terms of density, area, and shape. They can also be connected via a Delaunay triangulation, whose characterization in the noise-only situation permits, a contrario, to identify signals embedded in noise from “silent” points.
Keywords
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- Information
- Explorations in Time-Frequency Analysis , pp. 139 - 167Publisher: Cambridge University PressPrint publication year: 2018