Formulation of Multidimensional Frequency Characteristics of Second-Order Nonlinear IIR Filter

In this paper, the formulation of multidimensional frequency characteristics of a second-order nonlinear infinite impulse response (IIR) filter is presented. The second-order nonlinear IIR filter is based on a nonlinear differential equation for an electrodynamic loudspeaker and used to reduce nonlinear distortions of an electrodynamic loudspeaker. Hence, it is difficult to increase the filter order without considering the constraints of nonlinear differential equations to improve the capability of the filter to reduce nonlinear distortions. In this paper, the formulation of the frequency characteristics of the second-order nonlinear IIR filter is presented as a solution to this problem. This formulation is based on the principle of the second -order nonlinear IIR filter for reducing the nonlinear distortions. From this formulation, it is shown that the nonlinearities of the second-order nonlinear IIR filter can be represented by the multidimensional frequency characteristics, which is similar to Volterra filters with the feedback structure. The validity of the formulation is shown by comparing the frequency characteristics of the conventional nonlinear IIR filter structure with those of new formulated ones through some experiments.