Error surfaces of adaptive active noise controllers

It is shown that the shape of the error surface of an adaptive active noise control system in an arrangement where the input and output of the controller are not acoustically isolated from each other is strongly affected by reverberation in the acoustic system. An analytical expression is derived for the error surface of a particularly simple configuration (which nevertheless is believed to be sufficiently typical to have widespread applicability). Examples of plots of this expression are shown, and the implications for an adaptive system of the way in which the error surface changes shape as the amount of reverberation increases are spelled out