Multidimensional sampling of isotropically bandlimited signals
Journal article, 2018

A new lower bound on the average reconstruction error variance of multidimensional sampling and reconstruction is presented. It applies to sampling on arbitrary lattices in arbitrary dimensions, assuming a stochastic process with constant, isotropically bandlimited spectrum and reconstruction by the best linear interpolator. The lower bound is exact for any lattice at sufficiently high and low sampling rates. The two threshold rates where the error variance deviates from the lower bound gives two optimality criteria for sampling lattices. It is proved that at low rates, near the first threshold, the optimal lattice is the dual of the best sphere-covering lattice, which for the first time establishes a rigorous relation between optimal sampling and optimal sphere covering. A previously known result is confirmed at high rates, near the second threshold, namely, that the optimal lattice is the dual of the best sphere-packing lattice. Numerical results quantify the performance of various lattices for sampling and support the theoretical optimality criteria.

sampling theorem

volume visualization

Nyquist rate

multidimensional signal processing

sphere packing

sphere covering

Lattice theory


Erik Agrell

Chalmers, Electrical Engineering, Communication and Antenna Systems, Communication Systems

Balázs Csébfalvi

Budapest University of Technology and Economics

IEEE Signal Processing Letters

1070-9908 (ISSN)

Vol. 25 3 383-387

Areas of Advance

Information and Communication Technology

Subject Categories


Communication Systems

Signal Processing



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Latest update

5/8/2018 6