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| Content Provider | Springer Nature Link |
|---|---|
| Author | Saliani, Sandra |
| Copyright Year | 2010 |
| Abstract | Wavelet packets provide an algorithm with many applications in signal processing together with a large class of orthonormal bases of L 2(ℝ), each one corresponding to a different splitting of L 2(ℝ) into a direct sum of its closed subspaces. The definition of wavelet packets is due to the work of Coifman, Meyer, and Wickerhauser, as a generalization of the Walsh system. A question has been posed since then: one asks if a (general) wavelet packet system can be an orthonormal basis for L 2(ℝ) whenever a certain set linked to the system, called the “exceptional set” has zero Lebesgue measure. This answer to this question affects the quality of wavelet packet approximation. In this paper we show that the answer to this question is negative by providing an explicit example. In the proof we make use of the “local trace function” by Dutkay and the generalized shift-invariant system machinery developed by Ron and Shen. |
| Ending Page | 39 |
| Page Count | 25 |
| Starting Page | 15 |
| File Format | |
| ISSN | 01764276 |
| e-ISSN | 14320940 |
| Journal | Constructive Approximation |
| Issue Number | 1 |
| Volume Number | 33 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2010-07-10 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Generalized shift-invariant systems Local trace function Tight frame Analysis Numerical Analysis Wavelet packets Wavelets and other special systems |
| Content Type | Text |
| Resource Type | Article |
| Subject | Analysis Computational Mathematics |
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