Nonlinear Model and its Inverse of an Audio System

TL;DR

This thesis develops a nonlinear Volterra model for loudspeaker behavior and its inverse, trained with LMS algorithms, demonstrating improved accuracy over linear models based on measurements from a physical speaker.

Contribution

It introduces a Volterra series-based nonlinear model and its inverse for loudspeaker modeling, with training methodology and experimental validation.

Findings

Nonlinear Volterra model reduces mean squared error compared to linear models.

Model performance depends on test signal, model order, and parameters.

Inverse system trained with the same algorithm improves system control.

Abstract

This computer science master thesis aims at modelling the nonlinearities of a loudspeaker. A piecewise linear approximation is initially explored and then we present a nonlinear Volterra model to simulate the behavior of the system. The general theory of continuous and discrete Volterra series is summarised. A Normalized Least Mean Square algorithm is used to determine the Volterra series to third order. We also present as inverted system which is trained with the same algorithm. Training data for the models were collected measuring a physical speaker using a laser interferometer. Results indicate a decrease in Mean Squared Error compared to the linear model with a dependency on the particular test signal, the order and the parameters of the model.