Uncertainty principles, minimum uncertainty samplings and translations

Daniel Lantzberg*, Florian Lieb, Hans Georg Stark, Ron Levie, Nir Sochen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


It has been shown recently, that the conventional variance based uncertainty measure associated with the wavelet transform can be arbitrarily small. Hence, no global minimizer exists. In this paper we introduce a new discretization scheme in scale and time shifts, such that the total uncertainty of a corresponding function system has the lowest possible value. We also describe a generalized uncertainty principle inspired by the familiar uncertainty principle in time-frequency analysis. As an example we apply this concept to wavelet analysis, leading to a new affine uncertainty principle. We also introduce waveforms minimizing this principle. Furthermore, we remark that the uncertainty measure associated with this new principle allows for decay estimates of the ambiguity function (reproducing kernel) associated with the wavelet transform.

Original languageEnglish
Title of host publicationProceedings of the 20th European Signal Processing Conference, EUSIPCO 2012
Number of pages5
StatePublished - 2012
Event20th European Signal Processing Conference, EUSIPCO 2012 - Bucharest, Romania
Duration: 27 Aug 201231 Aug 2012

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491


Conference20th European Signal Processing Conference, EUSIPCO 2012


  • Uncertainty principle
  • harmonic analysis


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