Modelling of LIP radiation impedance in Z-domain

Three z-domain models for lip radiaton impedance are introduced. Two of them are based on the observation that the normalized acoustic impedance can be modelled as
z(\omega) = C*[1.-\cos(\omegaT)] + j*B*\sin(\omegaT)
. The values of the parameters C and B for different sampling frequencies and radiation areas are found by minimizing the mean square error (MSE) between the modelled and the acoustic impedance. Owing to the sine and cosine functions used, the modelled impedance can be transformed exactly and straightforwardly into the z-domain. The third model described is a pole-zero-model, the parameters of which are also optimized by MSE-criterion. The limits for acceptable errors of the modelled impedances are studied and the models compared to the well known Flanagan's model.