In this paper, we propose a 3rd-order nonlinear IIR filter for compensating nonlinear distortions of loudspeaker systems. Nonlinear distortions are common around the lowest resonance frequency for electrodynamic loudspeaker systems. One interesting approach to compensating nonlinear distortions is to employ a mirror filter. The mirror filter is derived from the nonlinear differential equation for loudspeaker systems. The nonlinear parameters of a loudspeaker system, which include the force factor, stiffness, and so forth, depend on the displacement of the diaphragm. The conventional filter structure, which is called the 2nd-order nonlinear IIR filter that originates the mirror filter, cannot reduce nonlinear distortions at high frequencies because it does not take into account the nonlinearity of the self-inductance of loudspeaker systems. To deal with this problem, the proposed filter takes into account the nonlinearity of the self-inductance and has a 3rd-order nonlinear IIR filter structure. Hence, this filter can reduce nonlinear distortions at high frequencies while maintaining a lower computational complexity than that of a Volterra filter-based compensator. Experimental results demonstrate that the proposed filter outperforms the conventional filter by more than 2dB for 2nd-order nonlinear distortions at high frequencies.

In this paper, we propose a parameter estimation method using Volterra kernels for the nonlinear IIR filters, which are used for the linearization of closed-box loudspeaker systems. The nonlinear IIR filter, which originates from a mirror filter, employs nonlinear parameters of the loudspeaker system. Hence, it is very important to realize an appropriate estimation method for the nonlinear parameters to increase the compensation ability of nonlinear distortions. However, it is difficult to obtain exact nonlinear parameters using the conventional parameter estimation method for nonlinear IIR filter, which uses the displacement characteristic of the diaphragm. The conventional method has two problems. First, it requires the displacement characteristic of the diaphragm but it is difficult to measure such tiny displacements. Moreover, a laser displacement gauge is required as an extra measurement instrument. Second, it has a limitation in the excitation signal used to measure the displacement of the diaphragm. On the other hand, in the proposed estimation method for nonlinear IIR filter, the parameters are updated using simulated annealing (SA) according to the cost function that represents the amount of compensation and these procedures are repeated until a given iteration count. The amount of compensation is calculated through computer simulation in which Volterra kernels of a target loudspeaker system is utilized as the loudspeaker model and then the loudspeaker model is compensated by the nonlinear IIR filter with the present parameters. Hence, the proposed method requires only an ordinary microphone and can utilize any excitation signal to estimate the nonlinear parameters. Some experimental results demonstrate that the proposed method can estimate the parameters more accurately than the conventional estimation method.