Abstract
We consider sampling strategies for a class of multivariate bandlimited functions f that have a spectrum consisting of disjoint frequency bands. Taking advantage of the special spectral structure, we provide formulas relating f to the samples f(y),y∈X, where X is a periodic nonuniform sampling set. In this case, we show that the reconstruction can be viewed as an iterative process involving certain Vandermonde matrices, resulting in a link between the invertibility of these matrices to the existence of certain sampling sets that guarantee a unique recovery. Furthermore, estimates of inverse Vandermonde matrices are used to provide explicit L2-stability estimates for the reconstruction of this class of functions.
Original language | English (US) |
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Pages (from-to) | 361-372 |
Number of pages | 12 |
Journal | Linear Algebra and Its Applications |
Volume | 555 |
DOIs | |
State | Published - Oct 15 2018 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
Keywords
- Inverse Vandermonde matrices
- Periodic nonuniform sampling
- Stable sampling