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We consider the extension of the Whittaker-Shannon interpolation reconstruction formula to the case of band-limited signals observed in the presence of correlated noise. Observing that in this situation the classical sampling expansion gives inconsistent reconstruction, we apply a postfiltering strategy yielding a smooth correction of the interpolation series. We assess the accuracy of the method by the global L2 error. A large class of dependent noise processes is taken into account. This includes short and long memory errors. Whereas the short memory errors have relatively small influence on the reconstruction accuracy, the long-memory errors can dramatically slow down the convergence rate. We explain this phenomenon by evaluating the speed at which the reconstruction error tends to zero.