Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T14:46:22.113Z Has data issue: false hasContentIssue false

5 - Uncertainty

from Part I - Basics and Constraints

Published online by Cambridge University Press:  22 August 2018

Patrick Flandrin
Affiliation:
École normale supérieure de Lyon
Get access

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).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Uncertainty
  • Patrick Flandrin
  • Book: Explorations in Time-Frequency Analysis
  • Online publication: 22 August 2018
  • Chapter DOI: https://doi.org/10.1017/9781108363181.007
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Uncertainty
  • Patrick Flandrin
  • Book: Explorations in Time-Frequency Analysis
  • Online publication: 22 August 2018
  • Chapter DOI: https://doi.org/10.1017/9781108363181.007
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Uncertainty
  • Patrick Flandrin
  • Book: Explorations in Time-Frequency Analysis
  • Online publication: 22 August 2018
  • Chapter DOI: https://doi.org/10.1017/9781108363181.007
Available formats
×