The all-pass filtered-x algorithm

The convergence speed of the filtered-x LMS algorithm is known to be slow due to the secondary acoustic path in front of the adaptive filter. Two methods are presented to improve the convergence properties of that algorithm. The exact method, referred to as the decor-related filtered-x algorithm, suffers from `the division by small number´ problem and an alternative approximate method is proposed. The approximate method, referred to as the all-pass filtered-x algorithm, avoids division by using only the phase information of the secondary acoustic path to generate the required filtered-x signal, which is equivalent to performing partial decorrelation. Performance comparison of the different algorithms shows that the all-pass filtered-x, although approximate, performs better than the decorrelated filtered-x.