Parameter Adaptation in Nonlinear Loudspeaker Models
Loudspeaker is a device that converts electric input signal to acoustic output. The most common type of loudspeaker is a moving-coil transducer. The behaviour of a moving-coil transducer can be considered to be linear only when displacement of the coil-diaphragm assembly is small. When input signal level rises, nonlinearities start to cause audible distortion. In this thesis we examine microspeaker, a small loudspeaker used in mobile phones. The electro-mechanical process which converts the electrical signal into sound waves is exaplained. Based on this, we present a continuous-time, linear model of a loudspeaker mounted in a closed box. The model describes the loudspeaker’s small-signal behaviour using only few parameters. We then consider the main sources of nonlinearities and how to model them. Two major sources nonlinearities are added to the continuous-time model. Then transformations from continuous-time models to discrete-time models are considered. The nonlinear model is converted to discrete-time while taking into account the properties of the microspeaker. The main purpose of this thesis is to study performance of a algorithm that ﬁnds the parameter values of the nonlinear loudspeaker model. Performance of the algorithm is compared to performance of an earlier algorithm for the linear loudspeaker model. The parameter values are found and changes in them are tracked using an adaptive signal processing method called system identiﬁcation. The parameter values are updated using LMS algorithm. Since the discrete-time mechanical model of the microspeaker is based on a recursive ﬁlter, LMS algorithm for recursive ﬁlters is presented. We also review previous research related to parameter identiﬁcation in linear and nonlinear loudspeaker models. Based on results from the experiments the studied algorithm is deemed to be yet incomplete. Linear parameters adapt in general quickly whereas the nonlinear parameters adapt too slowly and sometimes erroneously. The diﬀerence between the output predicted by the nonlinear loudspeaker model and the actual output of the loudspeaker (prediction error) is too high, meaning the parameters do not adapt to their true values. The model is also prone to instability. The algorithm requires further development regarding adaptation speed and prevention of instability. Other development considering initial parameter values and operation during silent moments should also be conducted in the future.