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Kernels for reconstructing nonideally sampled nonbandlimited signals

Deviating from classical Shannon-type sampling, we determine the MMSE-optimum reconstructions kernels for linearly interpolating a non-bandlimited signal from a discrete set of noisy measurements obtained from non-δ sampling kernels. For this purpose, the first and second order moment functions (ACF) of the continuous input process are required. We provide examples showing how the input autocorrelation, the sampling kernel, and the input noise level shape the form of the optimal interpolating kernels.