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
12 - Spectrogram Geometry 2
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
Spectrograms are revisited from a Bargmann transform point of view, with the time-frequency plane identified to the complex plane. This permits to establish simple phase-magnitude relationships for the Gaussian STFT and to describe reassignment via a vector field which happens to be the gradient of the associated (log-)spectrogram. This also paves the way to variations such as differential or adjustable reassignment. Within this picture, the whole reassignment process can be described in terms of attractors (maxima), repellers (zeros), and basins of attraction (component domains).
Keywords
- Type
- Chapter
- Information
- Explorations in Time-Frequency Analysis , pp. 106 - 115Publisher: Cambridge University PressPrint publication year: 2018