On linear systems disturbed by wide-band noise Agamirza E. Bashirov Department of Mathematics, Eastern Mediterranean University Gazimagusa, Mersin 10, Turkey
[email protected] Institute of Cybernetics, Azerbaijan Academy of Sciences F. Agayev St. 9, Baku-370141, Azerbaijan Keywords: Wide-band noise, white noise, stochastic sys- function £ is called an autocovariance function. The wide- tem, filtering. band noise process ³ is said to be stationary if the autoco- × " variance function £ depends only on (see [1]). If is so small that it is normally assumed to be 0, then the wide-band Abstract noise process ³ is transformed into a white noise process. As it was mentioned, in many fields such substitution gives rise An approach, based on a distributed delay, is presented to to tangible distortions. handle wide-band noise processes. This approach is closely There are different techniques of handling and working related with the semigroups of right translation and allows with the wide-band noise processes. For example, in [2] the a reduction of a wide-band noise driven linear system to a approximate approach is used. Another approach, based on white noise driven linear system. This reduction is applied a representation of wide-band noise as a distributed delay of to the Kalman-Bucy filtering in order to modify it to a wide- white noise, is suggested in [3]. band noise driven linear system. In [3, 4] the Kalman-Bucy estimation results are modified to a wide-band noise driven systems. The proofs of respec- tive results are based on the duality principle and, technically, 1 Introduction they are routine being useless if one tries to modify them to nonlinear systems.