Adaptive Filtering Theory And Applications Using The Delta Operator

Delta operator is a new discretization method that plays the important role in high-speed signal processing and digital sampled control. Delta operator approach can not only avoid the ill-conditioned problems caused by the conventional shift operator based theory when fast sampling, but also the delta operator formulated model approaches the corresponding continuous time model as the sampling interval goes to zero, thus the design method for continuous time systems can be directly applied to discrete time systems.The thesis is supported by the Natural Science Foundation of Henan Province entitled "Robust design for adaptive inverse control systems using delta operator" and Foundation for University Key Teacher by Henan Province entitled "Delta operator approach to adaptive inverse control design and performance analysis". Development of adaptive inverse control is firstly surveyed, then the problems of the delta operator formulated adaptive filtering theory and applications are studied. The major results of the thesis are as following.(1) The filtered-X and filtered- ? LMS algorithms are considered which are widely used in adaptive inverse control system. The performance analysis of the above two algorithms is given. Then the simpler matrix descriptions of LMS algorithm using delta operator are presented, the delta operator formulated filtered-X and filtered- ?LMS algorithms are also derived.(2) The filtering problem of the delta operator formulated LMS algorithm with QR decomposition (Delta-QR-LMS) is studied. The recursive formulae of the Delta-QR-LMS is developed, both the convergence and the stability of this algorithm are analyzed. Simulation results indicate Delta-QR-LMS algorithm has the advantages compared with Delta-LMS.(3) Delta operator model is introduced to the adaptive equalizer design. Updating-parameter expressions for decision feedback equalizer (DFE) based on delta operator are deduced. And the simulation results confirm the high effectiveness of proposed equalizer.