Research For A Adaptive LMS Algorithm With Variable Step Based N Multi-scale Wavelet Transform

Adaptive filtering theory is an important part in the field of signal processing.Adaptive filtering algorithm iS one of the most active research in modem signalprocessing field．Because of its simple, small burden and easing to realize,leastMean Square(LMS)algorithm based on steepest is used widely in adaptive filter． ButLMS algorithm big weakness is that its convergence speed is very slow.In order tospeedup the convergence process，one can increase the step size，but at the sallletime，the Steady state error will be large and the algorithm may even become unsta-ble．Fixed step size cannot result in fast convergence speed and low residual errorsimultaneously．In order to solve thisproblem，people present a lot of modified LMSalgorithms．There are two famous research direction of algorithms that are summa-rized，one is variable step size LMS algorithm，the other one is transform-domainLMS algorithm.The wavelet transform is known as "math microscope" of analysising signal hasthe good capacity to decrease the correlation property of the input vector，and pos-sesses the characteristics of multi-resolution and time-frequency localization,thewavelet transform also have the corresponding Mallat fast algorithm,so the multi-ple-scale wavelet transform theory is introduced into the LMS adaptive filtering al-gorithm.Theoretical analysis and simulations show that the WT-LMS algorithm con-verges faster than the classical LMS adaptive filtering．The spectrum dynamic rangeof auto-correlation matrix of the input vector is decreased SO that the convergencespeed of the LMS algorithm is improved．On the other hand, the novel algorithm Canresolve the contradiction that fixed step size cannot result in fast convergence speedand low residual error simultaneously．Experimental results demonstrate that the newalgorithm has not only better convergence property but also better stable mean squareerrors than the former algorithms．The variable step size LMS algorithm and the multiple-scale wavelet transformare merged into the adaptive filtering system.The novel algorithm iS applied to speechsignal noise cancellation system． Experimental results demonstrate that theWTVSLMS algorithm can overcome the deficiency of classical speech signal adaptivenoise cancellation system that has a slow convergence speed and a large maladjust-ment and the large spectrum dynamic range of auto-correlation matrix of the inputveetor．...