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17,857
RANDOM SAMPLING OF BANDLIMITED FUNCTIONS
, 2008
"... We consider the problem of random sampling for bandlimited functions. When can a bandlimited function f be recovered from randomly chosen samples f(xj), j ∈ J ⊂ N? We estimate the probability that a sampling inequality of the form ..."
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Cited by 2 (1 self)
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We consider the problem of random sampling for bandlimited functions. When can a bandlimited function f be recovered from randomly chosen samples f(xj), j ∈ J ⊂ N? We estimate the probability that a sampling inequality of the form
Fourier and Hankel Bandlimited Functions
"... The relationship between the sampling theorem associated with the Hankel transform and the sampling theorem associated with the Fourier transform is examined further. It is shown that a Fourier bandlimited function is also Hankel bandlimited under fairly general conditions. Key words and phrases  H ..."
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Cited by 4 (0 self)
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The relationship between the sampling theorem associated with the Hankel transform and the sampling theorem associated with the Fourier transform is examined further. It is shown that a Fourier bandlimited function is also Hankel bandlimited under fairly general conditions. Key words and phrases
APPROXIMATION OF BANDLIMITED FUNCTIONS BY EXPONENTIAL SUMS
"... Abstract. Let K be a compact set in Rn. For 1 ≤ p ≤ ∞, the Bernstein space BpK is the Banach space of all functions f ∈ Lp(Rn) such that its Fourier transform in a distributional sense is supported on K. If f ∈ BpK, then f is continuous on Rn and has an extension onto the complex space Cn to an enti ..."
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Abstract. Let K be a compact set in Rn. For 1 ≤ p ≤ ∞, the Bernstein space BpK is the Banach space of all functions f ∈ Lp(Rn) such that its Fourier transform in a distributional sense is supported on K. If f ∈ BpK, then f is continuous on Rn and has an extension onto the complex space Cn
Reconstruction of bandlimited functions from unsigned samples
 Journal of Fourier Analysis and Applications
, 2011
"... We consider the recovery of realvalued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samp ..."
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Cited by 5 (0 self)
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We consider the recovery of realvalued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible
Irregular Sampling of the Radon Transform of Bandlimited Functions
"... Abstract—We provide conditions for exact reconstruction of a bandlimited function from irregular polar samples of its Radon transform. First, we prove that the Radon transform is a continuous L2operator for certain classes of bandlimited signals. We then show that the BeurlingMalliavin condition f ..."
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Abstract—We provide conditions for exact reconstruction of a bandlimited function from irregular polar samples of its Radon transform. First, we prove that the Radon transform is a continuous L2operator for certain classes of bandlimited signals. We then show that the BeurlingMalliavin condition
Wave propagation using bases for bandlimited functions
 Wave Motion
, 2005
"... We develop a twodimensional solver for the acoustic wave equation with spatially varying coefficients. In what is a new approach, we use a basis of approximate prolate spheroidal wavefunctions and construct derivative operators that incorporate boundary and interface conditions. Writing the wave eq ..."
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Cited by 27 (4 self)
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We develop a twodimensional solver for the acoustic wave equation with spatially varying coefficients. In what is a new approach, we use a basis of approximate prolate spheroidal wavefunctions and construct derivative operators that incorporate boundary and interface conditions. Writing the wave equation as a firstorder system, we evolve the equation in time using the matrix exponential. Computation of the matrix exponential requires efficient representation of operators in two dimensions and for this purpose we use short sums of onedimensional operators. We also use a partitioned lowrank representation in one dimension to further speed up the algorithm. We demonstrate that the method significantly reduces numerical dispersion and computational time when compared with a fourthorder finite difference scheme in space and an explicit fourthorder Runge–Kutta solver in time.
Nonperiodic Sampling of Bandlimited Functions on Unions of Rectangular Lattices
, 1996
"... It is shown that a function f 2 L p [\GammaR; R], 1 p ! 1, is completely determined by the samples of f on sets = [ m i=1 fn=2r i g n2Z where R = P r i , and r i =r j is irrational if i 6= j, and of f (j) (0) for j = 1; : : : ; m \Gamma 1. If f 2 C m\Gamma2\Gammak [\GammaR; R], then t ..."
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Cited by 11 (1 self)
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It is shown that a function f 2 L p [\GammaR; R], 1 p ! 1, is completely determined by the samples of f on sets = [ m i=1 fn=2r i g n2Z where R = P r i , and r i =r j is irrational if i 6= j, and of f (j) (0) for j = 1; : : : ; m \Gamma 1. If f 2 C m\Gamma2\Gammak [\GammaR; R
Sampling of Bandlimited Functions on Unions of Shifted Lattices
 J. Fourier Anal. Appl
, 2000
"... We consider Shannon sampling theory for sampling sets which are unions of shifted lattices. These sets are not necessarily periodic. A function f can be reconstructed from its samples provided the sampling set and the support of the Fourier transform of f satisfy certain compatibility conditions. Wh ..."
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Cited by 9 (1 self)
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We consider Shannon sampling theory for sampling sets which are unions of shifted lattices. These sets are not necessarily periodic. A function f can be reconstructed from its samples provided the sampling set and the support of the Fourier transform of f satisfy certain compatibility conditions
SAMPLING EXPANSION OF BANDLIMITED FUNCTIONS OF POLYNOMIAL GROWTH ON THE REAL LINE
"... Abstract. For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line. 1. ..."
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Abstract. For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line. 1.
Results 1  10
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