Wigner measures in the discrete setting: high-frequency analysis of sampling & reconstruction operators
Macia, Fabricio
arXiv, 0307313 / Harvested from arXiv
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.
Publié le : 2003-07-23
Classification:  Mathematics - Numerical Analysis,  Mathematical Physics,  Mathematics - Functional Analysis,  42C15,  94A12,  65D05,  46E35,  46E39
@article{0307313,
     author = {Macia, Fabricio},
     title = {Wigner measures in the discrete setting: high-frequency analysis of
  sampling \& reconstruction operators},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0307313}
}
Macia, Fabricio. Wigner measures in the discrete setting: high-frequency analysis of
  sampling & reconstruction operators. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0307313/