Journal Article10.1109/18.45278
A stable nonuniform sampling expansion involving derivatives
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TL;DR: The work of D.A. Linden and N.M. Abramson is completed in the sense that a full investigation of the convergence properties of the expansion is made and a stability property is proved.
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Abstract: The work of D.A. Linden and N.M. Abramson (Inf. Control, vol.3, p.26-31, 1960, and vol.4, p.95-6, 1961) is completed in the sense that a full investigation of the convergence properties of the expansion is made. By adapting the work of N. Levinson (Am. Math. Soc. Colloq. Pub. vol.26, 1940) on nonharmonic Fourier series and general results from the theory of B-splines, the author extends the result to the case of sampling with uniformly spaced samples. A stability property is proved. >
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Citations
Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines
Karlheinz Gröchenig,Irina Shafkulovska +1 more
TL;DR: Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The conditions are near optimal and imply the existence of sampling sets with lower Beurling density arbitrarily close to the necessary density.
1
The ‘Riesz Basis Method’ for Deriving Sampling Series: An Overview and Some Applications
J. R. Higgins
- 01 Jan 2002
TL;DR: In this article, a method for finding Riesz sampling bases for classes of band-limited functions is presented, and its connections with stability of sampling, and with sample point density are described.
Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals
Kumari Priyanka,A. Antony Selvan +1 more
TL;DR: Derivative sampling expansions in shift-invariant spaces with error estimates covering discontinuous signals TLDR: A new type of polynomials based on derivative samples is introduced for approximating discontinuous signals in shift-invariant spaces. The rate of approximation is established in terms of $L^p$- average modulus of smoothness.
Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines
Karlheinz Gröchenig,Irina Shafkulovska +1 more
Undersampled Windowed Exponentials and Their Applications
Chun-Kit Lai,Sui Tang +1 more
TL;DR: In this article, the completeness and frame/basis properties of a union of under-sampled windowed exponentials were characterized by the spectra of the Toeplitz operators.
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