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Abstract: We study some problems related to the effect of bounded, additive samplenoise in the bandlimited interpolation given by theWhittaker-Shannon-Kotelnikov WSK sampling formula. We establish a generalizedform of the WSK series that allows us to consider the bandlimited interpolationof any bounded sequence at the zeros of a sine-type function. The main resultof the paper is that if the samples in this series consist of independent,uniformly distributed random variables, then the resulting bandlimitedinterpolation almost surely has a bounded global average. In this context, wealso explore the related notion of a bandlimited function with bounded meanoscillation. We establish some properties of such functions, and in particular,we show that they are either bounded or have unbounded samples at any positivesampling rate. We also discuss a few concrete examples of functions thatdemonstrate these properties.



Autor: Gaurav Thakur

Fuente: https://arxiv.org/



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