Existence of uncertainty minimizers for the continuous wavelet transform
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3105079Utgivelsesdato
2023Metadata
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- Institutt for matematiske fag [2360]
- Publikasjoner fra CRIStin - NTNU [37317]
Originalversjon
10.1002/mana.202100466Sammendrag
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.