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In this contribution we discuss the translation-invariant interpolation of frequency domain functions by means of a well-conditioned Gaussian-modulated pole kernel which generates exclusively stable poles. For the implementation we use an adaptive interpolation process which is a variant of a recently introduced adaptive residual subsampling method. It is shown that the interpolation process with the Gaussian-modulated pole kernel also provides an excellent pre-processing interface when used in conjunction with the popular vector fitting algorithm. This results in a composite algorithm, performing the sampling and modelling of the given frequency function in a fully automatic way.