Error surfaces and adaption behaviour of active noise control systems

Input mise characteristics Knowledge of the geometry of the error surface is essential to the understanding of any adaptive system, and especially for one using any form of gradient descent algorithm. Most adaptive active noise control systems in the published literature use one form or another of the LMS adaptive algorithm (either in its standard non-recursive form [ 13 or in Feintuch's extension to the recursive form [2]). Because this algorithm is an approximation to a steepest descent algorithm its performance is very strongly affwted by the {gradient of the error surface and if the eigenvalues of the performance surface have substantially differing magnitudes the cmnvergence rate that can be achieved is poor. The comparative simplicity of implementation of the algorithm, however, has so far been sufficient to make it the preferred candidate i n real systems. Number of Linearity of Feedback Acoustic control transmission from reverberation channels paths secondary present sowce(s) to &tector(s) It is a problem with many real systems that the dimensionality of the error surface is so great as to make it rather difficult to perceive their character. However in many cases the essence of the system can be captured using a grossly simplified model with only a few coefficients in the adaptive system (and hence an error surface whose dimension is reasonably small). Input mise characteristics sinusoidal quasi-stationary periodic non-stationary random The following parameters may be used to separate active noise control systems into classes having different complexities. The variety of these classes is indicated in the following (rather arbitrary) table; in each case the complexity will generally increase from top to bottom of a column. Each column is of course independent of all the others so the table indicates that there are perhaps 324 significantly different complexities of active noise control system. Number of Linearity of Feedback Acoustic control transmission from reverberation channels paths secondary present sowce(s) to &tector(s)