Optimal filtering with multirate observations

This paper considers the problem of optimal filtering for several channels of observations occurring at different sampling rates. The problem is formulated in general terms with arbitrary sampling rates for the observations. The set of observation sequences (channels) are jointly cyclostationary and the resulting optimal filters are linear and periodically time-varying (LPTV). A formula for the period of the system is given and the explicit forms of the Wiener-Hopf equations and the estimation error variance are derived. Simulation results are presented for estimation of a signal with known correlation function in noise using two observation sequences with sampling rates differing from that of the underlying signal to be estimated.