Identification of Loudspeakers Using Fractional Derivatives
When small loudspeakers reproduce audio at high volumes, the resulting degradation requires the use of equalization and linearization to attain quality. This requires accurate modeling and identification of the loudspeaker. As described previously, a technique based on polynomial state-space representation can be used in the loudspeaker identification process because it encompasses both the linear and nonlinear characteristics in one compact model. The nonlinear part, which is added to the linear part, is described by combination of cross-products of state and input variables. In order to reduce the complexity of this task, the loudspeaker model was split into two cascading parts: the electromechanical motor that transforms the input audio into displacement and the mechanico-acoustic component that transforms the displacement into an acoustic wave. In this paper, the authors show that the electrical impedance of the motor can be properly modeled and identified as a Fractional Order (FO) system. Experimental results demonstrate that the FO approach results in both a lower fitting error and a smaller order compared to the traditional integer order approach.
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