Abstract
The approximation of problems in \(d\) spatial dimensions by trigonometric polynomials supported on known more or less sparse frequency index sets \(I\subset \mathbb {Z}^d\) is an important task with a variety of applications. The use of rank-1 lattices as spatial discretizations offers a suitable possibility for sampling such sparse trigonometric polynomials. Given an arbitrary index set of frequencies, we construct rank-1 lattices that allow a stable and unique discrete Fourier transform. We use a component-by-component method in order to determine the generating vector and the lattice size.
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