منابع مشابه
Random Sampling of Bandlimited Functions
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 A‖f‖ 2 ≤ ∑ j∈J |f(xj)| ≤ B‖f‖2 hold uniformly for all functions f ∈ L(R) with supp f̂ ⊆ [−1/2, 1/2] or for some subset of bandlimited functions. In contrast to discret...
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We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, n...
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Functions of bounded mean oscillation (BMO) play an important role in complex function theory and harmonic analysis. In this paper a sampling theorem for bandlimited BMO-functions is derived for sampling points that are the zero sequence of some sine-type function. The class of sinetype functions is large and, in particular, contains the sine function, which corresponds to the special case of e...
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The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids {kT + Tn}k∈Z with offsets {Tn}n=1 ⊂ [0, T ]. If the offsets Tn are chosen independently and uniformly at random from [0, T ] and if the sample values of f are quantized with a first or...
متن کاملSampling of bandlimited functions on unions of shifted lattices
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. While explicit reconstruction formulas are possible, it is most convenient to use a recursive algor...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2010
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-010-0036-7