Tracking of a time-varying acoustic impulse response by an adaptive filter

A simple model is set up describing roughly the change of an acoustic impulse response if an object moves through a room. From this model, specifications can be formed regarding the length and convergence rate of an adaptive filter trying to track this change. It is shown that in many practical applications an adaptive filter would not perform better than the optimal fixed filter. Next, a more accurate model is set up for the change of an acoustic impulse response if an object moves through a room. An expression is worked out for the performane of a certain type of adaptive filter, the so-called LMS adaptive filter, in tracking this change for the case of white noise as input signal to the filter. It is shown that when the nonstationaries are due to a person walking through a normal living room, and the system has the bandwidth of speech or larger, an LMS adaptive filter cannot perform substantially better than a fixed filter. This result is in agreement with the results obtained with the simple model