The paper presents a mathematical theory of handling and working with wideband noises. We demonstrate that a wideband noise can be represented as a distributed delay of a white noise. From this, we deduce that the behavior of a wideband noise is the 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 and also to derive nonlinear filtering equation for wideband-noise-driven linear and nonlinear systems. Copyright © 2012 John Wiley & Sons, Ltd.