Essay On Adaptive Filters

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Adaptive filters have been successfully applied to diverse fields including communications, speech recognition, control systems, radar, seismology and biomedical engineering. Among various types of adaptive algorithms, the least-mean-square (LMS) algorithm is well known and widely adopted due to its simplicity and robustness to initial condition and noise. The performance of the LMS algorithm, in terms of convergence rate, maladjustment, mean-square error (MSE), and computational cost, is governed by the step- size. The frequency-domain (FD) adaptive filter algorithm is known to be able to reduce the numerical complexity by using the overlap-and-save implementation method. It incorporates block updating strategies where the fast Fourier …show more content…

A variable step-size algorithm is proposed in,by focusing on achieving low residual error specifically for the acoustic echo cancellation applications and also lacks of convergence analysis. Thus, we are motivated to develop an FD step-size control for LMS algorithm. Our objective is to achieve both fast convergence and low steady-state error, and to provide theoretical analysis on the convergence. A new bin-wise block-varying step size for the FD LMS algorithm. The optimal solution of step size at each iteration is derived by cancelling the a posteriori error in each frequency bin, and its estimate is connected to the magnitude-squared coherence (MSC) function. This Performs better than the existing FD algorithm in terms of both convergence rate and mean square deviation (MSD). Furthermore, compared to the TD algorithm, the proposed method converges faster in the presence highly of correlated filter input. 5.1.1 frequency-Domain Variable Step-Size LMS The derivation of the proposed FD step size control algorithm,

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