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Optimal lattices for sampling

Hans R. Künsch ; Erik Agrell (Institutionen för signaler och system, Kommunikationssystem) ; Fred A. Hamprecht
IEEE Transactions on Information Theory (0018-9448). Vol. 51 (2005), 2, p. 634-647.
[Artikel, refereegranskad vetenskaplig]

The generalization of the sampling theorem to multidimensional signals is considered, with or without bandwidth constraints. The signal is modeled as a stationary random process and sampled on a lattice. Exact expressions for the mean-square error of the best linear interpolator are given in the frequency domain. Moreover, asymptotic expansions are derived for the average mean-square error when the sampling rate tends to zero and infinity, respectively. This makes it possible to determine the optimal lattices for sampling. In the low-rate sampling case, or equivalently for rough processes, the optimal lattice is the one which solves the packing problem, whereas in the high-rate sampling case, or equivalently for smooth processes, the optimal lattice is the one which solves the dual packing problem. In addition, the best linear interpolation is compared with ideal low-pass filtering (cardinal interpolation).

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Denna post skapades 2006-09-12. Senast ändrad 2016-04-28.
CPL Pubid: 11977

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Kommunikationssystem

Ämnesområden

Information Technology

Chalmers infrastruktur