An Almost Sure Result on Sampling of Bandlimited Random Signals

The Shannon-Nyquist sampling theorem for deterministic signals is a fundamental result in the field of telecommunication and signal processing, and many results on this topic have been obtained. However, very few results on random signals have been published, after Kolmogorov mentioned the importance of Shannon-formula for stochastic signals in 1956. In this paper, following the almost sure result for bandlimited stochastic processes proposed by Seip in 1990, we give an almost sure result of the classical sampling theorem for bandlimited random signals with local average sampling.