Sampling and reconstruction in shift-invariant spaces on $$\mathbb {R}^d$$ R d
| LEADER | caa a22 4500 | ||
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| 001 | 605496099 | ||
| 003 | CHVBK | ||
| 005 | 20210128100534.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10231-014-0439-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0439-x | ||
| 245 | 0 | 0 | |a Sampling and reconstruction in shift-invariant spaces on $$\mathbb {R}^d$$ R d |h [Elektronische Daten] |c [A. Selvan, R. Radha] |
| 520 | 3 | |a Let $$\phi \in W(C,\ell ^1)$$ ϕ ∈ W ( C , ℓ 1 ) such that $$\{\tau _n\phi :n\in \mathbb {Z}^d\}$$ { τ n ϕ : n ∈ Z d } forms a Riesz basis for $$V(\phi )$$ V ( ϕ ) . It is shown that $$\mathbb {Z}^d$$ Z d is a stable set of sampling for $$V(\phi )$$ V ( ϕ ) if and only if $$\Phi ^\dagger (x)\ne 0$$ Φ † ( x ) ≠ 0 , for every $$x\in \mathbb {T}^d$$ x ∈ T d , where $$\Phi ^{\dagger }(x):=\sum _{n\in \mathbb {Z}^d}\phi (n)e^{2\pi in\cdot x},~~ x\in \mathbb {T}^d$$ Φ † ( x ) : = ∑ n ∈ Z d ϕ ( n ) e 2 π i n · x , x ∈ T d . Sampling formulae are provided for reconstructing a function $$f\in V(\phi )$$ f ∈ V ( ϕ ) from uniform samples using Zak transform and complex analytic technique. The problem of sampling and reconstruction is discussed in the case of irregular samples also. The theory is illustrated with some examples, and numerical implementation for reconstruction of a function from its nonuniform samples is provided using MATLAB. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Frames |2 nationallicence | |
| 690 | 7 | |a Laurent operator |2 nationallicence | |
| 690 | 7 | |a Riesz basis |2 nationallicence | |
| 690 | 7 | |a Shift-invariant space |2 nationallicence | |
| 690 | 7 | |a Wiener amalgam space |2 nationallicence | |
| 690 | 7 | |a Zak transform |2 nationallicence | |
| 700 | 1 | |a Selvan |D A. |u Department of Mathematics, Indian Institute of Technology Madras, 600 036, Chennai, India |4 aut | |
| 700 | 1 | |a Radha |D R. |u Department of Mathematics, Indian Institute of Technology Madras, 600 036, Chennai, India |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1683-1706 |x 0373-3114 |q 194:6<1683 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0439-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0439-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Selvan |D A. |u Department of Mathematics, Indian Institute of Technology Madras, 600 036, Chennai, India |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Radha |D R. |u Department of Mathematics, Indian Institute of Technology Madras, 600 036, Chennai, India |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1683-1706 |x 0373-3114 |q 194:6<1683 |1 2015 |2 194 |o 10231 | ||