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
5 - Uncertainty
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
Gaussian functions happen also to be central with respect to the intrinsic conflict that exists between time and frequency and which is referred to as “uncertainty.” This can take various forms depending upon the chosen measure of spread or occupancy in both domains. The striking feature is that most of the intuitive measures such as dispersion or entropy end up with Gaussians as minimizers, making them “quanta” of information (“logons” in Gabor's terminology).
Keywords
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- Chapter
- Information
- Explorations in Time-Frequency Analysis , pp. 35 - 39Publisher: Cambridge University PressPrint publication year: 2018