UC San Diego

In this note, the concept of wide-band noise is analyzed via a certain integral representation. It is proved that there are infinitely many wide-band noise processes represented in integral form which correspond to the same autocovariance function. Based on this integral representation, a technique of reduction of a wide-band noise driven system to a white noise driven system is presented. This technique is used to modify the separation principle and the Kalman–Bucy filtering to wide-band noise driven systems.