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Delay structure of wideband noises with application to filtering problems
Author(s) -
Bashirov Agamirza,
Mazhar Zeka,
Etikan Hüseyin,
Ertürk Sinem
Publication year - 2012
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.1029
Subject(s) - wideband , noise (video) , nonlinear system , computer science , kalman filter , colors of noise , white noise , filter (signal processing) , nonlinear filter , control theory (sociology) , mathematics , acoustics , electronic engineering , telecommunications , physics , engineering , filter design , artificial intelligence , image (mathematics) , computer vision , control (management) , quantum mechanics
SUMMARY 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.