Error-free filtering of entropy-regular process against a background of entropy-singular noise

It is shown that X(t) (and hence Z(t)) at any instant t can be correctly reconstructed from the observations Y_←∞ ^t={Y(s),s⩽t}, where X(t) and Z(t) are independent entropy-regular and entropy-singular stationary processes, respectively, and Y(t)=X(t)+Z(t). The particular interest in the filtering theory of random processes is the case where the error-free filtering is possible. It is also shown that the error-free filtering is also possible if X(t) and Z(t) are entropy-regular and entropy-singular processes, respectively, i.e., if Z(t) belongs to the significantly more extensive class processes than one with a singular spectrum