On the Prediction of a Class of Wide-Sense Stationary Random Processes

We prove that under suitable conditions, a multi-band wide sense stationary stochastic process can be linearly predicted at time t with arbitrarily small error using past samples taken at uniform rate. This result generalizes previous similar results for band-limited signals. Moreover we prove that the prediction problem from uniform past samples is equivalent to a disjoint translates condition on the spectrum together with the divergence of a logarithmic integral. We also show that, for the band-limited case, under similar conditions, non uniform samples can be taken.