Kernel-Induced Sampling Theorem for Translation-Invariant Reproducing Kernel Hilbert Spaces with Uniform Sampling

Akira Tanaka

ICASSP 2018accepted0 citations

Kernel-Induced Sampling Theorem for Translation-Invariant Reproducing Kernel Hilbert Spaces with Uniform Sampling

Abstract

The kernel-induced sampling theorem enables us to determine whether the sampling theorem holds or not for a reproducing kernel Hilbert space and a given set of sampling points. However, it is not easy to specifically calculate the necessary and sufficient condition formula except in some special cases, since it includes the inverse of an infinite dimensional Gramian matrix. In this paper, we discuss the kernel-induced sampling theorem restricted to a translation-invariant reproducing kernel Hilbert space with uniform sampling; and introduce an alternative necessary and sufficient condition formula, in which the inverse of the Gramian matrix is explicitly treated, by incorporating the theory of Laurent operators.

BibTeX

@inproceedings{icassp2018_kernelinducedsam,
  title = {Kernel-Induced Sampling Theorem for Translation-Invariant Reproducing Kernel Hilbert Spaces with Uniform Sampling},
  author = {Akira Tanaka},
  booktitle = {ICASSP 2018},
  year = {2018}
}