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The Origins of the Sampling Theorem
"... the two revolutionary papers in which he founded the information theory [1, 2]. In [1] the sampling theorem is formulated as “Theorem 13”: Let f(t) contain no frequencies over W. Then ∞ sin π ( 2Wt−n) f() t = ∑ Xn ..."
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Cited by 7 (0 self)
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the two revolutionary papers in which he founded the information theory [1, 2]. In [1] the sampling theorem is formulated as “Theorem 13”: Let f(t) contain no frequencies over W. Then ∞ sin π ( 2Wt−n) f() t = ∑ Xn
ON THE MULTIDIMENSIONAL SAMPLING THEOREM
"... Abstract. The well known sampling theorem is extended to the multidimensional weakly stationary (but not necessarily bandlimited) processes. The mean square and almost sure convergence of the sampling expansion sum is derived for full spectrum multidimensional processes. 1. ..."
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Abstract. The well known sampling theorem is extended to the multidimensional weakly stationary (but not necessarily bandlimited) processes. The mean square and almost sure convergence of the sampling expansion sum is derived for full spectrum multidimensional processes. 1.
The Kramer sampling theorem revisited
"... Abstract The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide ..."
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Abstract The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we
Nonstationary Processes and the Sampling Theorem
 IEEE Signal Processing Letters
, 2001
"... In [1], a sampling theorem for nonstationary random processes is developed, under the condition that the twodimensional (2D) power spectrum (2DPS) of the process has compact support. In this letter, it is shown that, for 2 ( ) processes, only a onedimensional (1D) restriction on the marginal a ..."
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Cited by 3 (2 self)
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In [1], a sampling theorem for nonstationary random processes is developed, under the condition that the twodimensional (2D) power spectrum (2DPS) of the process has compact support. In this letter, it is shown that, for 2 ( ) processes, only a onedimensional (1D) restriction on the marginal
Sampling theorems for the Heisenberg group
, 2008
"... In the first part of the paper a general notion of sampling expansions for locally compact groups is introduced, and its close relationship to the discretisation problem for generalised wavelet transforms is established. In the second part, attention is focussed on the simply connected nilpotent Hei ..."
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Heisenberg group H. We derive criteria for the existence of discretisations and sampling expansions associated to lattices in H. Analogies and differences to the sampling theorem over the reals are discussed, in particular a notion of bandwidth on H will figure prominently. The main tools
Kernelinduced sampling theorem
 IEEE Transactions on Signal Processing (in printing
"... Abstract—A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is discussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to perfectly recover the functions is obtained i ..."
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subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points. Index Terms—Gramian matrix, Hilbert space, orthogonal projection, reproducing kernel, sampling theorem. I.
On the Classical . . . SHANNON SAMPLING THEOREM
"... We proceed with our recentlyintroduced geometric approach to sampling of manifolds and investigate the relationship that exists between the classical, i.e. Shannon type, and geometric sampling concepts and formalism. Some aspects of coding and the Gaussian channel problem are considered. A geometr ..."
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geometric version of Shannon’s Second Theorem is introduced. Applications to Pulse Code Modulation and Vector Quantization of Images are provided. An extension of our sampling scheme to a certain class of infinite dimensional manifolds is also considered. The relationship between real functions of bounded
SHANNON SAMPLING THEOREM
"... Abstract. We proceed with our recentlyintroduced geometric approach to sampling of manifolds and investigate the relationship that exists between the classical, i.e. Shannon type, and geometric sampling concepts and formalism. Some aspects of coding and the Gaussian channel problem are considered. ..."
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. A geometric version of Shannon’s Second Theorem is introduced. Applications to Pulse Code Modulation and Vector Quantization of Images are provided. An extension of our sampling scheme to a certain class of infinite dimensional manifolds is also considered. The relationship between real functions
Sampling theorems and compressive sensing on the sphere
"... We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a bandlimited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling theore ..."
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We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a bandlimited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling
Interpolating Multiwavelet Bases and the Sampling Theorem
, 1999
"... This paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal (interpolating). They also showed that th ..."
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Cited by 24 (3 self)
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This paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal (interpolating). They also showed
Results 1  10
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2,163