The conventional algorithms in the echo canceling system have drawback when they are faced with double-talk condition in noisy environment. Since the double-talk and noise signal are exist, then the error signal is contaminated to estimate the gradient correctly. In this paper, we define a new class of adaptive algorithm for tap adaptations, based on the correlation function processing. The computer simulation results show that the Correlation LMS (CLMS) and the Extended CLMS (ECLMS) algorithms have better performance than conventional LMS algorithm. In order to implement the ECLMS algorithm, the Frequency domain Extended CLMS (FECLMS) algorithm is proposed to reduce the computational complexity. However the convergence speed is not sufficient. In order to improve the convergence speed, the Wavelet domain Extended CLMS (WECLMS) algorithm is proposed. The computer simulation results support the theoretical findings and verify the robustness of the proposed WECLMS algorithm in the double-talk situation.