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Average sampling and reconstruction for reproducing kernel stochastic signals. (English) Zbl 1372.94382

Summary: This paper mainly considers the problem of reconstructing a reproducing kernel stochastic signal from its average samples. First, a uniform convergence result for reconstructing the deterministic reproducing kernel signals by an iterative algorithm is established. Then, we prove that the quadratic sum of the corresponding reconstructed functions is uniformly bounded. Moreover, the reconstructed functions provide a frame expansion in the special case \(p=2\). Finally, the mean square convergence for recovering a weighted reproducing kernel stochastic signal from its average samples is given under some decay condition for the autocorrelation function, which can be removed for the case \(p=2\).

MSC:

94A20 Sampling theory in information and communication theory
60G35 Signal detection and filtering (aspects of stochastic processes)
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References:

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