Oversampling, quasi-affine frames, and wave packets (Q1433016)
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scientific article; zbMATH DE number 2075388
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Oversampling, quasi-affine frames, and wave packets |
scientific article; zbMATH DE number 2075388 |
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Oversampling, quasi-affine frames, and wave packets (English)
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15 June 2004
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Two families \(\{f_n\},\{g_n\}\) of elements in a Hilbert space \(H\) form a reproducing system if \(f= \sum \langle f,g_n\rangle f_n\) for all \(f\in H\). Three of the authors of the present paper previously obtained characterizations of reproducing systems of a very general type, including wavelet systems and Gabor systems; here these results are applied to study the effect of oversampling of shift-invariant systems and wavelet systems. As for the known (but less general) results in the literature, the considered type of oversampling preserves the frame bounds.
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affine systems
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frames
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Gabor systems
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oversampling
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quasi-affine systems
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wavelets
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0.88367164
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0.8551672
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0.8536538
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0.85030067
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0.84513617
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