Multivariate sampling theorems associated with multiparameter differential operators
M. H. Annaby
- 01 Jun 2005
- Vol. 48, Iss: 2, pp 257-277
TL;DR: In this paper, the multivariate sampling theory associated with multiparameter eigenvalue problems is investigated, and a several-variable counterpart of the classical sampling theorem of Whittaker, Kotel'nikov and Shannon is given.
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Abstract: We investigate the multivariate sampling theory associated with multiparameter eigenvalue problems. A several-variable counterpart of the classical sampling theorem of Whittaker, Kotel'nikov and Shannon is given. It arose when the multiparameter system has order one. Two-dimensional sam- pling theorems associated with two-parameter systems of second-order differential operators will be established. The sampling formulae are of multivariate non-uniform Lagrange interpolation type. Unlike many of the known formulae, the interpolating functions are not necessarily products of single variable functions.
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Citations
•Book
Sampling Theory in Signal and Image Processing
Laurent Fesquet,Bruno Torrésani +1 more
- 01 Jan 2011
TL;DR: Ten papers were accepted, covering a wide range of aspects of sampling theory and applications and applications (impulse radio ultra-wide band, non-uniform sampling and filtering, multichannel sampling), including classical sampling, frame theory, wavelets, and applications.
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Multivariate sampling theorems associated with multiparameter differential operators
M. H. Annaby
- 01 Jun 2005
TL;DR: In this paper, the multivariate sampling theory associated with multiparameter eigenvalue problems is investigated, and a several-variable counterpart of the classical sampling theorem of Whittaker, Kotel'nikov and Shannon is given.
Accurate sampling formula for approximating the partial derivatives of bivariate analytic functions
R. M. Asharabi,Jürgen Prestin +1 more
TL;DR: This paper applies the bivariate sinc-Gauss sampling formula to approximate partial derivatives of any order for entire and holomorphic functions on an infinite horizontal strip domain using only finitely many samples of the function itself.
3
Series Expansion for Functions Bandlimited to a Ball
L. Lorne Campbell
- 01 Jan 2008
TL;DR: In this article, an expansion related to the sampling theorem is derived for functions with Fourier transforms that vanish outside a ball in d dimensions, where the number of measurements per unit volume is equal to the Nyquist-Landau density.
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The Approximation of Eigencurves by Sampling
Abdullah Alazemi,Fares Alazemi,Amin Boumenir +2 more
- 01 May 2013
TL;DR: In this paper, the sampling method was extended to deal with the computation of eigenvalues of Sturm-Liouville systems and the 2-dimensional sampling theorem was used to find a representation for eigencurves, which are easily approximated by computing a finite matrix of size N × N and its truncation error is of order.
2
References
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Fourier Transforms in the Complex Domain
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Approximation of Functions of Several Variables and Imbedding Theorems
Sergei Mihailovic Nikol’skii
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