Adaptive knot placement for rational spline interpolation of sparse EM-based data

Frequency domain interpolation methods suffer poor numerical conditioning when the frequency range or the model order becomes large. Therefore, an earlier developed modeling technique, called AFS [T. Dhaene, 2002], is extended by using smart piece-wise rational interpolation with adaptive knot placement. The AFS algorithm is used to model the spectral response of general passive planar electrical structures over a frequency range of interest, based on a limited number of data samples. The new algorithm adoptively chooses an appropriate sample distribution, while minimizing the complexity of the model and the number of splines, without any prior knowledge of the dynamics of the system.