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
13 - The Noise Case
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
When applied to white Gaussian noise, Gaussian spectrograms are made of patches whose distribution is controlled by the correlation function of the STFT considered as a 2D homogeneous field, and in turn by the underlying reproducing kernel of the analysis. This can be given a simple model whose basic ingredients are a mean distribution of logons resulting from a circle packing argument due to uncertainty, and an adequate degree of randomness in fluctuations around the mean model and inter-logon phase relationships.
- Type
- Chapter
- Information
- Explorations in Time-Frequency Analysis , pp. 116 - 123Publisher: Cambridge University PressPrint publication year: 2018