A new fast adaptive filtering algorithm was presented by using the correlations between the signal’s former and latter sampling times. The proof of the new algorithm was also presented

which showed that its optimal weight vector was the solution of generalized Wiener equation. The new algorithm was of simple structure

fast convergence

less stable maladjustment. It had the ability of dealing with many signals

including noncorrelation signal and strong correlation signal. However

its computational complexity was comparable to that of NLMS algorithm. Simulation results show that for noncorrelation signal

the stable maladjustment of the proposed algorithm is less than that of VS-NLMS algorithm

and its convergence is comparable to that of the algorithm proposed in reference but faster than that of L.E-LMS algorithm. For high correlation signal

its performance is superior to those of NLMS algorithm and DCR-LMS algorithm.