Behavior of the practically implemented filtered reference LMS algorithm in an active noise control system

A filtered-reference LMS algorithm is often used in practical active noise control systems. This algorithm is derived under the assumption of a stationary noise signal, and the order of the signal convolution is switched in the derivation process. However, the order of convolution cannot be changed in a real physical process. We examine the differences between these situations, i.e., theoretical formulation compared to practical control process, for various kinds of noise signals. Amplitude-modulated and low-pass noise signals are used as examples of disturbance signals. Results of the numerical simulations indicated that the practical implementation of the algorithm requires severer conditions for the convergence coefficient than those in the theoretical prediction. Analytical examination with the transformed coefficient update procedure also reveals the difference between them. To reduce this difference and achieve robust attenuation under practical conditions, a modified version of a filtered-reference LMS algorithm is introduced. Advantages of this modified version are verified through a series of simulations.