The tap-length and tap-weight adjusting problems of adaptive filter are converted into a single tap-weight adjusting problem. Based on this, a general tap-length updating formula and a new variable tap-length LMS algorithm are presented. The rationality and convergence property of the new algorithm are analyzed. The new algorithm uses time-mean square error to estimate steady state mean square error of the long and short filter and employs adaptive tap-length step size, thus it can update the tap-length fast before the tap-weight converges. It is also proved that several existing variable tap-length algorithms in the literatures can be regarded as special cases of the general updating formula. The theory analysis and numerical simulation results verify the new algorithm.
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