Research And Application Of Adaptiye Filtering Algorithms

The adaptive filters constitute an important part of the statistical signal processing.Currently, the study of adaptive filtering algorithms, which directly determine thefiltering performance, is one of the most active research topics in the field of adaptivesignal processing. Researchers constantly strive to seek fast convergence, low comput-ational complexity and robust adaptive filtering algorithms.Based on the basic principle of adaptive filters, this thesis introduce the presentmain adaptive filtering algorithms and their applications. The LMS algorithm is deeplyanalyzed.Aiming at the conflict between the convergence rate and stable state mean squareerror of fixed step LMS algorithm, using the information of instantaneous error squareand instantaneous error correlation, integrating the advantage of the VSS algorithm andthe MVSS algorithm, a variable step adaptive algorithm is given. The stable perfor-mance and tracking ability are analyzed theoretically. The simulation results show thatthis algorithm has faster convergence rate and lower stable state square error. Applied tothe fetal ECG extraction, this algorithm has an important theoretical value and practicalsignificance.At the same time, consider of the shortcomings of the LMS algorithms, a kind offuzzy variable step-size adaptive algorithms is presented and applied to harmonic detect-ion, by using the fuzzy control theory.