Application Of Wiener Series For Assessment Of The Quality Of The NARMAXModel Of Dynamic Loudspeakers

Abstract

The polynomial representation of the NARMAX model of a dynamic loudspeaker is presented. To compare different models one needs a quality criterion. The simplest quality measure is the difference between the model output signals and the object (the actual loudspeaker) output signals if the same input signal is used. But this measure provides no information about the characteristics of either the model or the actual loudspeaker. The information can be obtained from the Volterra series or from its orthogonal version called the Wiener series. The latter has been applied to an actual loudspeaker and its NARMAX model. Euclid's norm was used to determine the difference between the Wiener series of the loudspeaker and that of its model. The model's accuracy was verified for dynamic loudspeaker GDN 20140 excited by a signal with an electrical power of 30 watts. An optimized NARMAX model was created for the loudspeaker. Wiener kernels of the first (linear), second and third order were computed for the loudspeaker and its model. The difference between the NARMAX model's kernels and those of the loudspeaker did not exceed a few percent. This proves that the quality of the NARMAX model is very good.