Adaptive Interpolation Based on PÓlya Frequency Functions

Translation-invariant interpolation of frequency domain functions by means of Fourier transforms of Polya frequency functions, which belong to the Bochner class of interpolation kernels, is presented. For the implementation, we use an adaptive interpolation process which is a variant of the recently introduced adaptive residual subsampling method. Moreover, it is shown that adaptive residual subsampling with Polya interpolation kernels is an excellent preprocessing interface when used in conjunction with the well-known vector fitting (VF) rational modeling algorithm.