OPTIMAL FILTRATION OF PERIODIC PROCESSES.

An examination is made of optimal mean square filtration of a periodic signal of arbitrary form in the presence of random noises. It is assumed that the form of the signal is either known, or random with known statistical moments of the coefficients in its expansion in a trigonometric series. The noise contains a white component and a correlated component. The filter memory is assumed to be finite, and equal to, or a multiple of, the period of the input process. Under these conditions, simple analytic expressions are found for the weight function of an optimal filter and for its mean square error.