Book contents
- Frontmatter
- Dedication
- Contents
- Acknowledgements
- Preface
- Notation
- 1 Introduction
- Part I Basics and Constraints
- 2 Small Data Are Beautiful
- 3 Of Signals and Noise
- 4 On Time, Frequency, and Gauss
- 5 Uncertainty
- 6 From Time and Frequency to Time-Frequency
- 7 Uncertainty Revisited
- 8 On Stationarity
- Part II Geometry and Statistics
- References
- Index
7 - Uncertainty Revisited
from Part I - Basics and Constraints
Published online by Cambridge University Press: 22 August 2018
Book contents
- Frontmatter
- Dedication
- Contents
- Acknowledgements
- Preface
- Notation
- 1 Introduction
- Part I Basics and Constraints
- 2 Small Data Are Beautiful
- 3 Of Signals and Noise
- 4 On Time, Frequency, and Gauss
- 5 Uncertainty
- 6 From Time and Frequency to Time-Frequency
- 7 Uncertainty Revisited
- 8 On Stationarity
- Part II Geometry and Statistics
- References
- Index
Summary
As Fourier images of (modified) ambiguity functions, time-frequency energy distributions obey uncertainty relations that can take different forms, depending on the chosen measure of spread in the plane (e.g., norms, support, variance, or entropy). In complement to classical formulations of uncertainty, this reinforces the role played by Gaussians and Gaussian STFTs/spectrograms.
- Type
- Chapter
- Information
- Explorations in Time-Frequency Analysis , pp. 50 - 55Publisher: Cambridge University PressPrint publication year: 2018