<b>Problem statement:</b> In this study, we proposed a new algorithm M-SMFTF for adaptive filtering with fast convergence and low complexity. <b>Approach</b>: It was the result of a simplified FTF type algorithm, where the adaptation gain was obtained only from the forward prediction variables and using a new recursive method to compute the likelihood variable. <b>Results:</b> The computational complexity was reduced from 7L-6L, where L is the finite impulse response filter length. Furthermore, this computational complexity can be significantly reduced to (2L+4P) when used with a reduced P-size forward predictor. <b>Conclusion</b>: This algorithm presented a certain interest, for the adaptation of very long filters, like those used in the problems of echo acoustic cancellation, due to its reduced complexity, its numerical stability and its convergence in the presence of the speech signal
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