Fourier supports of scaling functions determine cardinalities of wavelets (Q2911898)
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scientific article; zbMATH DE number 6075902
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourier supports of scaling functions determine cardinalities of wavelets |
scientific article; zbMATH DE number 6075902 |
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3 September 2012
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mother wavelets
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scaling functions
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multiresolution analysis
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cardinality
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Fourier supports of scaling functions determine cardinalities of wavelets (English)
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This paper studies a pair of dual frame multiresolution analyses (MRA's) with dilation matrix \(S\). The author proves some formulae on the number of mother wavelets. It turns out that the cardinality is determined by the supports of Fourier transforms of the scaling functions. Based on these formulae, the author constructs quasi-biorthogonal frame wavelets with minimal cardinality.
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