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| Format: | Preprint |
| Publicat: |
2003
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/math/0307313 |
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| _version_ | 1866917022743396352 |
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| author | Macia, Fabricio |
| author_facet | Macia, Fabricio |
| contents | The goal of this article is that of understanding how the oscillation and concentration effects developed by a sequence of functions in $\mathbb{R}^{d} $ are modified by the action of Sampling and Reconstruction operators on regular grids. Our analysis is performed in terms of Wigner and defect measures, which provide a quantitative description of the high frequency behavior of bounded sequences in $L^{2}(mathbb{R}^{d}) $. We actually present explicit formulas that make possible to compute such measures for sampled/reconstructed sequences. As a consequence, we are able to characterize sampling and reconstruction operators that preserve or filter the high-frequency behavior of specific classes of sequences. The proofs of our results rely on the construction and manipulation of Wigner measures associated to sequences of discrete functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0307313 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | Wigner measures in the discrete setting: high-frequency analysis of sampling & reconstruction operators Macia, Fabricio Numerical Analysis Mathematical Physics Functional Analysis 42C15; 94A12; 65D05; 46E35; 46E39 The goal of this article is that of understanding how the oscillation and concentration effects developed by a sequence of functions in $\mathbb{R}^{d} $ are modified by the action of Sampling and Reconstruction operators on regular grids. Our analysis is performed in terms of Wigner and defect measures, which provide a quantitative description of the high frequency behavior of bounded sequences in $L^{2}(mathbb{R}^{d}) $. We actually present explicit formulas that make possible to compute such measures for sampled/reconstructed sequences. As a consequence, we are able to characterize sampling and reconstruction operators that preserve or filter the high-frequency behavior of specific classes of sequences. The proofs of our results rely on the construction and manipulation of Wigner measures associated to sequences of discrete functions. |
| title | Wigner measures in the discrete setting: high-frequency analysis of sampling & reconstruction operators |
| topic | Numerical Analysis Mathematical Physics Functional Analysis 42C15; 94A12; 65D05; 46E35; 46E39 |
| url | https://arxiv.org/abs/math/0307313 |