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Robust algorithms applied in Acoustic Echo Cancellation systems present an excessive calculation load that has to be minimized. In the present paper, we propose two different low complexity fast least squares algorithms, called Partial Update Simplified Fast Transversal Filter (PU-SMFTF) algorithm and Reduced Partial Update Simplified Fast Transversal Filter (RPU-SMFTF) algorithm. The first algorithm reduces the computational complexity in both filtering and prediction parts using the M-Max method for coefficients selection. Moreover, the second algorithm applies the partial update technique on the filtering part, joined to the P-size forward predictor, to get more complexity reduction. The obtained results show a computational complexity reduction from (7L+8) to (L+6M+8) and from (7L+8) to (L+M+4P+17) for the PU-SMFTF algorithm and RPU-SMFTF algorithm, respectively compared to the original Simplified Fast Transversal Filter (SMFTF). Furthermore, experiments picked out in the context of acoustic echo cancellation, have demonstrated that the proposed algorithms provide better convergence speed, good tracking capability and steady-state performances than the NLMS and SMFTF algorithms.

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