Abstract
We consider and analyse sampling theories in the reproducing kernel Hilbert space (RKHS) in this paper. The reconstruction of a function in an RKHS from a given set of sampling points and the reproducing kernel of the RKHS is discussed. Firstly, we analyse and give the optimal approximation of any function belonging to the RKHS in detail. Then, a necessary and sufficient condition to perfectly reconstruct the function in the corresponding RKHS of complex-valued functions is investigated. Based on the derived results, another proof of the sampling theorem in the linear canonical transform (LCT) domain is given. Finally, the optimal approximation of any band-limited function in the LCT domain from infinite sampling points is also analysed and discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 109-120 |
| Number of pages | 12 |
| Journal | European Journal of Applied Mathematics |
| Volume | 26 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 3 Feb 2015 |
Keywords
- Linear canonical transform (LCT)
- Reproducing kernel Hilbert space (RKHS)
- Sampling theorem