  We study some problems related to the effect of bounded, additive sample
noise in the bandlimited interpolation given by the
Whittaker-Shannon-Kotelnikov (WSK) sampling formula. We establish a generalized
form of the WSK series that allows us to consider the bandlimited interpolation
of any bounded sequence at the zeros of a sine-type function. The main result
of the paper is that if the samples in this series consist of independent,
uniformly distributed random variables, then the resulting bandlimited
interpolation almost surely has a bounded global average. In this context, we
also explore the related notion of a bandlimited function with bounded mean
oscillation. We establish some properties of such functions, and in particular,
we show that they are either bounded or have unbounded samples at any positive
sampling rate. We also discuss a few concrete examples of functions that
demonstrate these properties.
