Wide band noise as a distributed delay of white-noise

Abstract

The paper presents a mathematical theory of handling and working with wide band noises. We demonstrate that a wide band noise can be represented as a distributed delay of a white noise. Based on this we deduce that the behavior of a wide band noise is same as the behavior of an infinite dimensional colored noise along the boundary line. All these are used to deduce a complete set of formulae for the Kalman type optimal filter for a wide band noise driven linear systems.