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2010

Irregular Sampling on Shift Invariant Spaces

9 years 24 days ago
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
Kil Hyun Kwon, Jaekyu Lee
Added 26 Jan 2011
Updated 26 Jan 2011
Type Journal
Year 2010
Where IEICET
Authors Kil Hyun Kwon, Jaekyu Lee
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