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A new blind signal separation (BSS) technique is proposed, enabling a deterministic separation of signals into rational functions. Rational functions can take on a wide range of forms, such as the well-known pole-like shape. The approach is a possible alternative for the well-known independent component analysis when the theoretical sources are not independent, such as for frequency spectra, or when only a small number of samples is available. The technique uses a low-rank decomposition on the tensorized version of the observed data matrix. The deterministic tensorization with Löwner matrices is comprehensively analyzed in this paper. Uniqueness properties are investigated, and a connection with the separation into exponential polynomials is made. Finally, the technique is illustrated for fetal electrocardiogram extraction and with an application in the domain of fluorescence spectroscopy, enabling the …