SAMPLING EXPANSION IN SHIFT INVARIANT SPACES
2008 ◽
Vol 06
(02)
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pp. 223-248
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Keyword(s):
For any ϕ(t) in L2(ℝ), let V(ϕ) be the closed shift invariant subspace of L2(ℝ) spanned by integer translates {ϕ(t - n) : n ∈ ℤ} of ϕ(t). Assuming that ϕ(t) is a frame or a Riesz generator of V(ϕ), we first find conditions under which V(ϕ) becomes a reproducing kernel Hilbert space. We then find necessary and sufficient conditions under which an irregular or a regular shifted sampling expansion formula holds on V(ϕ) and obtain truncation error estimates of the sampling series. We also find a sufficient condition for a function in L2(ℝ) that belongs to a sampling subspace of L2(ℝ). Several illustrating examples are also provided.
2015 ◽
Vol 23
(1)
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pp. 115-126
2011 ◽
Vol 09
(03)
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pp. 417-426
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2012 ◽
Vol 10
(01)
◽
pp. 1250003
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2007 ◽
Vol 05
(05)
◽
pp. 753-767
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2006 ◽
Vol 04
(03)
◽
pp. 547-557
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2000 ◽
Vol 11
(03)
◽
pp. 515-524
2004 ◽
Vol 134
(6)
◽
pp. 1177-1197
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