Journal article
Minimality of the Data in Wavelet Filters
Advances in mathematics (New York. 1965), Vol.159(2), pp.143-228
05/10/2001
DOI: 10.1006/aima.2000.1958
Abstract
Orthogonal wavelets, or wavelet frames, for L2(R) are associated with quadrature mirror filters (QMF), a set of complex numbers which relate the dyadic scaling of functions on R to the Z-translates. In this paper, we show that generically, the data in the QMF-systems of wavelets are minimal, in the sense that the data cannot be nontrivially reduced. The minimality property is given a geometric formulation in the Hilbert space ℓ2(Z), and it is then shown that minimality corresponds to irreducibility of a wavelet representation of the algebra O2; and so our result is that this family of representations of O2 on the Hilbert space ℓ2(Z) is irreducible for a generic set of values of the parameters which label the wavelet representations.
Details
- Title: Subtitle
- Minimality of the Data in Wavelet Filters
- Creators
- Palle E.T Jorgensen - Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, Iowa, 52242-1419, f1E-mail: jorgen@math.uiowa.eduf1
- Resource Type
- Journal article
- Publication Details
- Advances in mathematics (New York. 1965), Vol.159(2), pp.143-228
- DOI
- 10.1006/aima.2000.1958
- ISSN
- 0001-8708
- eISSN
- 1090-2082
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 05/10/2001
- Academic Unit
- Mathematics
- Record Identifier
- 9983985830202771
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