Existence of uncertainty minimizers for the continuous wavelet transform

Simon Halvdansson, Jan Fredrik Olsen, Nir Sochen, Ron Levie

Research output: Contribution to journalArticlepeer-review


Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wavelet uncertainty functional. Recently, two new wavelet uncertainty functionals were derived from theoretical foundations. In both approaches, the uncertainty of a mother wavelet describes its concentration, or accuracy, as a time-scale probe. While an uncertainty minimizing mother wavelet can be proven to have desirable localization properties, the existence of such a minimizer was never studied. In this paper, we prove the existence of minimizers for the two uncertainty functionals.

Original languageEnglish
Pages (from-to)1156-1172
Number of pages17
JournalMathematische Nachrichten
Issue number3
StatePublished - Mar 2023


  • continuous wavelet
  • uncertainty minimizer
  • uncertainty principle
  • wavelet design

All Science Journal Classification (ASJC) codes

  • General Mathematics


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