Multiple-input multiple-output sampling: necessary density conditions
TL;DR: The notions of joint upper and lower densities for collections of sampling sets are introduced and necessary conditions on these densities are derived for stable sampling and consistent reconstruction of the channel inputs from the sampled outputs.
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Abstract: We consider the problem of multiple-input multiple-output (MIMO) sampling of multiband signals. In this problem, a set of input signals is passed through a MIMO channel modeled as a known linear time-invariant system. The inputs are modeled as multiband signals whose spectral supports are sets of finite measure and the channel outputs are sampled on nonuniform sampling sets. The aim is to reconstruct the inputs from the output samples. This sampling scheme is quite general and it encompasses various others including Papoulis' generalized sampling and nonuniform sampling as special cases. We introduce notions of joint upper and lower densities for collections of sampling sets and then derive necessary conditions on these densities for stable sampling and consistent reconstruction of the channel inputs from the sampled outputs. These results generalize classical density results for stable sampling and interpolation due to Landau.
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References
Generalized sampling expansion
TL;DR: In this article, it was shown that a band-limited function f(t) is uniquely determined in terms of the samples g_k(nT) of the responses of m linear systems with input f (t), sampled at 1/m the Nyquist rate.
733
•Book
Sampling theory in Fourier and signal analysis : foundations
J. R. Higgins
- 01 Jan 1996
TL;DR: In this article, the authors present an algorithm for the optimal regular sampling rate in the context of Paley-Weiner spaces, which is a generalization of the sampling theorem.
Sampling, data transmission, and the Nyquist rate
Henry Landau
- 01 Oct 1967
TL;DR: It is argued that only stable sampling is meaningful in practice, and it is proved that stable sampling cannot be performed at a rate lower than the Nyquist, and data cannot be transmitted as samples at a Rate of 2W per second, regardless of the location of sampling instants, the nature of the set of frequencies which the signals occupy, or the method of construction.
499
Sampling Theory in Fourier and Signal Analysis
John R. Higgins
- 30 May 1996
TL;DR: Sampling theory in Fourier and signal analysis book comprehensively covers sampling theory with a wide variety of topics.
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