Nonlinear modeling of loudspeaker using Adaptive Second order Volterra Filters

Linear modeling of nonlinear systems like equalizers, loudspeaker etc is not acceptable in practical situations. In this paper, the nonlinear state space model of the loudspeaker is considered as an unknown nonlinear system and is identified by adaptive second order Volterra filters (ASVF). The adaptations were done by using normalized least mean square (NLMS) and recursive least squares (RLS) algorithms. While cascading two SVFs, better approximation of the original system is obtained i.e. three harmonics of the input frequency are obtained at the output as compared to one harmonic with a single SVF. Experimental verification of the simulation results is done by identifying unknown non-linear system comprising of a loud speaker using adaptive second order Volterra filter. During the identification process, it is observed that the eigen value spread of the input correlation matrix and the bulk delay of 6.2 msec, introduced by the nonlinear system had a significant impact on the convergence of the adaptation algorithms. It is found that RLS algorithm converged after 200 iterations as compared to NLMS algorithm which took 500 iterations converge.