Multidimensional Irregular Sampling of Band-Limited Functions in Lp-Spaces
It is the purpose of this note to present a qualitative approach to irregular variants of the so-called Sampling theorem for band-limited functions on ℝm. The basic assertion is the following: Given a compact subset Ω ⊆ ℝm there is critical sampling rate δ0=δ0(Ω) > 0 such thatany band-limited f ∈ LP(ℝm) with spec f ⊆ Ω can be completely reconstructed from the sampling values (f(xi)i∈I at any δ0-dense discrete family of points X = (xi)i∈I. The reconstruction will be obtained by an iterative procedure yielding a sequence of smooth approximations of f, convergent to f in the LP-sense for 1 ≤ p < ∞.
KeywordsSampling Theorem Convolution Product Smooth Approximation Compact Neighborhood Voronoi Region
Unable to display preview. Download preview PDF.
- Butzer,P. W.SplettstöBer and R.L.Stens (1988): The sampling theorem and linear prediction in signal analysis. Jber.d.Dt.Math.-Ver. 90, 1–70.Google Scholar
- Feicht i nger, H.G. (1988): Discretization of convolution and reconstruction of band-limited functions from irregular sampling. To appear.Google Scholar
- Feic h tinger, H.G. and K.Gröchenig (1989): Reconstruction of band-limited functions from irregular sampling values. To appear.Google Scholar
- Feichtinger, H.G. and K.Gröchenig (1989): Irregular sampling theorems and series expansions of band-limited functions. To appear.Google Scholar
- Marvasti, F.A. (1987): A unified approach to zero-crossing and nonuniform sampling of single and multi-dimensional systems. Nonuniform. P.O.Box 1505, Oak Park, IL 60304.Google Scholar
- Trieb e 1,H. (1983): Theory of Function spaces. Akad.Verlagsges.,Leipzig 1983.Google Scholar
- Young, R: An Introduction to Nonharmonic Fourier Series. Acad.Press, New York, 1980.Google Scholar