Irregular Sampling on Shift Invariant Spaces

Let V (φ) be a shift invariant subspace of L2 (R) generated by a Riesz or frame generator φ(t) in L2 (R). We assume that φ(t) is suitably chosen so that V (φ) becomes a reproducing kernel Hilbert space on which the regular sampling expansion f(t) = n∈Z f(n)S(t − n), f ∈ V (φ) holds. Now we perturb the sampling points {n : n ∈ Z} to be {n + δn : n ∈ Z} and find conditions on the generator φ(t) and various bounds for the perturbation {δn : n ∈ Z} under which an irregular sampling expansion f(t) = n∈Z f(n + δn)Sn(t), f ∈ V (φ) holds. The results obtained here unity and improve some previous results on the same topic by others. KEY WORDS : SHIFT INVARIANT SPACE, RIESZ BASIS, FRAME, IRREGULAR SAMPLING EXPANSION REFERENCES

• Type: Journal
• Year: 2010
• Where: IEICET
• Authors: Kil Hyun Kwon, Jaekyu Lee
• Keywords: IEICET 2010, Regular Sampling Expansion, Reproducing Kernel Hilbert Space, Sampling Expansion