Generalized Sampling Series Approximation of Random Signals from Local Averages

Signals are often of random character since they cannot bear any information if they are predictable for any time t, they are usually modelled as stationary random processes. On the other hand, because of the inertia of the measurement apparatus, measured sampled values obtained in practice may not be the precise value of the signal X（t） at time tk（ k∈ Z）, but only local averages of X（t） near tk, In this paper, it is presented that a wide （or weak ） sense stationary stochastic process can be approximated by generalized sampling series with local average samples.