Journal ArticleDOI
On sampling in shift invariant spaces
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TLDR
A necessary and sufficient condition for sampling in the general framework of shift invariant spaces is derived and an improved estimate for the perturbation is derived for theperturbation of regular sampling in shift invariants spaces.Abstract:
A necessary and sufficient condition for sampling in the general framework of shift invariant spaces is derived. Then this result is applied, respectively, to the regular sampling and the perturbation of regular sampling in shift invariant spaces. A simple necessary and sufficient condition for regular sampling in shift invariant spaces is attained. Furthermore, an improved estimate for the perturbation is derived for the perturbation of regular sampling in shift invariant spaces. The derived estimate is easy to calculate, and shown to be optimal in some shift invariant spaces. The algorithm to calculate the reconstruction frame is also presented.read more
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Journal ArticleDOI
Convolution, Average Sampling, and a Calderon Resolution of the Identity for Shift-Invariant Spaces
TL;DR: In this article, the convolution/deconvolution problem, the uniformly sampled convolution and the reconstruction problem, and the sample convolution followed by sampling on irregular grid were studied.
Journal ArticleDOI
Local reconstruction for sampling in shift-invariant spaces
TL;DR: The proofs of the results on the local sampling and reconstruction in the refinable shift-invariant space V(ϕ) depend heavily on the linear independent shifts of a refinable function on measurable sets with positive Lebesgue measure and the almost ripplet property for a refinables function, which are new and interesting by themselves.
Journal ArticleDOI
Shift-Invariant and Sampling Spaces Associated With the Fractional Fourier Transform Domain
Ayush Bhandari,Ahmed I. Zayed +1 more
TL;DR: Two definitions of the discrete fractional Fourier transform and two semi-discrete fractional convolutions associated with them are introduced and used to derive necessary and sufficient conditions pertaining to FrFT domain, under which integer shifts of a function form an orthogonal basis or a Riesz basis for a shift-invariant space.
Journal ArticleDOI
On Lower Bounds for the Capacity of Deletion Channels
TL;DR: This correspondence considers binary deletion channels, where bits are deleted independently with probability d; it improves upon the framework used to analyze the capacity ofbinary deletion channels established by Diggavi and Grossglauser, improving on their lower bounds.
Journal ArticleDOI
Dual frames in L2(0,1) connected with generalized sampling in shift-invariant spaces
TL;DR: In this paper, the authors derived stable generalized sampling in a shift-invariant space by using some special dual frames in L 2 ( 0, 1 ), which involve samples of filtered versions of the functions in the shift invariant space.
References
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