Sampling and Frequency Warping
| Autor: | Lafon, Stefan, Véhel, Jacques Lévy, Peyrière, Jacques |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of frequencies, the function is transformed into a band-limited one. One may then perform a decomposition in Fourier series. This process gives rise to new orthonormal bases of the Sobolev spaces H^alpha. When alpha is an integer, these orthonormal bases can be expressed in terms of Laguerre functions. We study the reconstruction and speed of convergence properties of the warping-based sampling. Besides theoretical considerations, numerical experiments are performed. Comment: 21 pages, 10 figures |
| Databáze: | arXiv |
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