The predictability of band-limited, high-frequency and mixed processes in the presence of ideal low-pass filters

Pathwise predictability of continuous-time processes is studied in a deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study the possibility of approximation of convolution integrals over future time by integrals over past time. We found that all band-limited processes are predictable in this sense as well as high-frequency processes with zero energy at low frequencies. It follows that a process of mixed type can still be predicted if an ideal low-pass filter exists for this process.