Advances in Shannon's Sampling Theory

@inproceedings{Zayed1993AdvancesIS,
  title={Advances in Shannon's Sampling Theory},
  author={Ahmed I. Zayed},
  year={1993}
}
  • A. Zayed
  • Published 23 July 1993
  • Mathematics
Introduction and a Historical Overview. Shannon Sampling Theorem and Band-Limited Signals. Generalizations of Shannon Sampling Theorems. Sampling Theorems Associated with Sturm-Liouville Boundary-Value Problems. Sampling Theorems Associated with Self-Adjoint Boundary-Value Problems. Sampling by Using Green's Function. Sampling Theorems and Special Functions. Kramer's Sampling Theorem and Lagrange-Type Interpolation in N Dimensions. Sampling Theorems for Multidimensional Signals-The Feichtinger… 
Sampling in a Hilbert space
An analog of the Whittaker-Shannon-Kotel'nikov sampling theorem is derived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a
An Asymptotic Sampling Recomposition Theorem for Gaussian Signals
TLDR
The Shannon’s sampling theorem is generalized for a class of non band–limited signals which plays a central role in the signal theory, the Gaussian map is the unique function which reachs the minimum of the product of the temporal and frecuential width.
Sampling expansions for discrete transforms and their relationship with interpolation series
Kramer's sampling theorem gives us the possibility to reconstruct integral transforms from their values at sequences of real numbers. It is known that this theorem includes the
Sampling Theorem Associated with a Dirac Operator and the Hartley Transform
Abstract Kramer's sampling theorem indicates that, under certain conditions, sampling theorems associated with boundary-value problems involving n th order self-adjoint differential operators can be
Recent Progress of Shannon Sampling Theory with Applications
Errors appear when the Shannon sampling series is applied to approximate a signal in practice since the measured sampled values are usually given by averages of a function or the sampled values with
Shannon-Type Sampling Theory on Unions of Equally Spaced and Noncommensurate Grids
  • T. Moore
  • Computer Science, Mathematics
  • 2001
TLDR
The fundamental result in sampling theory known as "Shannon's sampling theorem" has many applications to signal processing and communications engineering and is demonstrated via complex interpolation methods.
Error Analysis for Shannon Sampling Series Approximation with Measured Sampled Values
TLDR
The uniform truncated error bound of Shannon series approximation for multivariate Besov class is obtained and the results show this kind of Shannonseries can approximate a smooth signal well.
ON SAMPLING AND SECOND ORDER DIFFERENCE EQUATIONS
Recently a discrete version of Kramer's sampling theorem has been developed. The new theorem allows us to derive sampling expansions associated with difference equations instead of differential
Finite lagrange and cauchy sampling expansions associated with regular difference equations
We use a discrete version of Kramer's sampling theorem to derive sampling expansions for discrete transforms whose kernels arise from regular difference equations. The kernels may be taken to be
...
...