Optimal reconstruction of periodically sampled signals with probabilistic timing delays

A periodic sampling process can be modelled through multiple parallel uniform sampling processes with distinct timing delays. In this paper, these timing delays are considered as random variables with known discrete probability density functions. An optimal reconstruction method, which minimizes the expected time-averaged mean squared error, is developed using a multirate filter bank structure. A design example is presented with simulation results demonstrating the superior performance of this method over standard reconstruction techniques based on deterministic timing delay models.