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首页> 外文期刊>Information Theory, IEEE Transactions on >Discrete Sampling and Interpolation: Universal Sampling Sets for Discrete Bandlimited Spaces
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Discrete Sampling and Interpolation: Universal Sampling Sets for Discrete Bandlimited Spaces

机译：离散采样和插值：离散带限空间的通用采样集

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摘要

We study the problem of interpolating all values of a discrete signal $f$ of length $N$ when $d < N$ values are known, especially in the case when the Fourier transform of the signal is zero outside some prescribed index set ${cal J}$; these comprise the (generalized) bandlimited spaces $BBB^{cal J}$. The sampling pattern for $f$ is specified by an index set ${cal I}$, and is said to be a universal sampling set if samples in the locations ${cal I}$ can be used to interpolate signals from $BBB^{cal J}$ for any ${cal J}$. When $N$ is a prime power we give several characterizations of universal sampling sets, some structure theorems for such sets, an algorithm for their construction, and a formula that counts them. There are also natural applications to additive uncertainty principles.
机译：我们研究了在已知$ d

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