OPTIMAL RECONSTRUCTION OF ARMA SIGNALS WITH DECIMATED SAMPLES UNDER CORRUPTING NOISE BY USE OF MULTIRATE KALMAN FILTER

A multirate modeling theory of the ARMA stochastic signals is derived from a state-space viewpoint in this work. Its application to the signal reconstruction problem for the recovery of the complete ARMA signal from its noise-corrupted, missing-sample sequence is then developed in detail, The proposed estimation-interpolation problem can be resolved by using the multirate optimal, state estimation scheme of this work. Theoretically, the multirate Kalman reconstruction filters derived in this paper produce the minimum variance estimation and interpolation of the original complete, clean ARMA signal. Practically, the numerical examples show that the multirate Kalman reconstruction filters illustrate good estimation/interpolation performances, not only for synthetic ARMA sequences but also for human speech signals.