
NuHAG :: TALKS
Talks given at NuHAG events






Deconvolution Based Analysis of Perturbed Integer Sampling in ShiftInvariant Spaces Niklas Grip Department of Mathematics, LuleĆ„ University of Technology SWEDEN given at strobl07 (17.06.07) id: 613 length: min status: accepted type: poster LINKPresentation: ABSTRACT:
An important cornerstone of both wavelet and sampling theory is _shiftinvariant_spaces_, that is, spaces spanned by a Riesz basis of integertranslates of a single function phi, which is referred to as _interpolating_ if phi(n)=delta_{0,n} for integers n.
Under some mild differentiability and decay assumptions on The Fourier transform phi^, we show that \varphi is interpolating and generates a shiftinvariant space V if and only if there is a deconvolution phi =g*chi_{[pi,pi]} for a certain function g with integral one.
Further, we exploit this fact in combination with analysis techniques introduced in a previous paper to derive jitter bounds epsilon = sup_k epsilon_k for which any f in V can be reconstructed from perturbed integer samples f(k+epsilon_k).
Finally, we demonstrate the resulting sampling theorem, for example, for some Meyertype phi and for compactly supported positive g with bounded variation.
The presented results are joint work with Stefan Ericsson.
